@article{8793,
abstract = {We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff.},
author = {Zeiner, Martin and Schmid, Ulrich and Chatterjee, Krishnendu},
issn = {0166218X},
journal = {Discrete Applied Mathematics},
number = {1},
pages = {392--415},
publisher = {Elsevier},
title = {{Optimal strategies for selecting coordinators}},
doi = {10.1016/j.dam.2020.10.022},
volume = {289},
year = {2021},
}
@inproceedings{9296,
abstract = { matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.},
author = {Aichholzer, Oswin and Arroyo Guevara, Alan M and Masárová, Zuzana and Parada, Irene and Perz, Daniel and Pilz, Alexander and Tkadlec, Josef and Vogtenhuber, Birgit},
booktitle = {15th International Conference on Algorithms and Computation},
isbn = {9783030682101},
issn = {16113349},
location = {Virtual},
pages = {221--233},
publisher = {Springer Nature},
title = {{On compatible matchings}},
doi = {10.1007/978-3-030-68211-8_18},
volume = {12635},
year = {2021},
}
@article{9293,
abstract = {We consider planning problems for graphs, Markov Decision Processes (MDPs), and games on graphs in an explicit state space. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems with k different target sets: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in a given sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds, based on the boolean matrix multiplication (BMM) conjecture and strong exponential time hypothesis (SETH), establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs, and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) problem-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.},
author = {Chatterjee, Krishnendu and Dvořák, Wolfgang and Henzinger, Monika and Svozil, Alexander},
issn = {00043702},
journal = {Artificial Intelligence},
number = {8},
publisher = {Elsevier},
title = {{Algorithms and conditional lower bounds for planning problems}},
doi = {10.1016/j.artint.2021.103499},
volume = {297},
year = {2021},
}
@article{9311,
abstract = {Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function. },
author = {Chatterjee, Krishnendu and Saona Urmeneta, Raimundo J and Ziliotto, Bruno},
issn = {0364-765X},
journal = {Mathematics of Operations Research},
keywords = {Management Science and Operations Research, General Mathematics, Computer Science Applications},
publisher = {Institute for Operations Research and the Management Sciences},
title = {{Finite-memory strategies in POMDPs with long-run average objectives}},
doi = {10.1287/moor.2020.1116},
year = {2021},
}
@phdthesis{8934,
abstract = {In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management.
We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.},
author = {Goharshady, Amir Kafshdar},
issn = {2663-337X},
pages = {278},
publisher = {IST Austria},
title = {{Parameterized and algebro-geometric advances in static program analysis}},
doi = {10.15479/AT:ISTA:8934},
year = {2021},
}
@inproceedings{8193,
abstract = {Multiple-environment Markov decision processes (MEMDPs) are MDPs equipped with not one, but multiple probabilistic transition functions, which represent the various possible unknown environments. While the previous research on MEMDPs focused on theoretical properties for long-run average payoff, we study them with discounted-sum payoff and focus on their practical advantages and applications. MEMDPs can be viewed as a special case of Partially observable and Mixed observability MDPs: the state of the system is perfectly observable, but not the environment. We show that the specific structure of MEMDPs allows for more efficient algorithmic analysis, in particular for faster belief updates. We demonstrate the applicability of MEMDPs in several domains. In particular, we formalize the sequential decision-making approach to contextual recommendation systems as MEMDPs and substantially improve over the previous MDP approach.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Karkhanis, Deep and Novotný, Petr and Royer, Amélie},
booktitle = {Proceedings of the 30th International Conference on Automated Planning and Scheduling},
issn = {23340843},
location = {Nancy, France},
pages = {48--56},
publisher = {Association for the Advancement of Artificial Intelligence},
title = {{Multiple-environment Markov decision processes: Efficient analysis and applications}},
volume = {30},
year = {2020},
}
@inproceedings{8272,
abstract = {We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME∩coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies.},
author = {Chatterjee, Krishnendu and Katoen, Joost P and Weininger, Maximilian and Winkler, Tobias},
booktitle = {International Conference on Computer Aided Verification},
isbn = {9783030532901},
issn = {16113349},
pages = {398--420},
publisher = {Springer Nature},
title = {{Stochastic games with lexicographic reachability-safety objectives}},
doi = {10.1007/978-3-030-53291-8_21},
volume = {12225},
year = {2020},
}
@inproceedings{8533,
abstract = {Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Ismael R and Svoboda, Jakub},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science},
isbn = {9783959771597},
issn = {18688969},
location = {Prague, Czech Republic},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Simplified game of life: Algorithms and complexity}},
doi = {10.4230/LIPIcs.MFCS.2020.22},
volume = {170},
year = {2020},
}
@inproceedings{8534,
abstract = {A regular language L of finite words is composite if there are regular languages L₁,L₂,…,L_t such that L = ⋂_{i = 1}^t L_i and the index (number of states in a minimal DFA) of every language L_i is strictly smaller than the index of L. Otherwise, L is prime. Primality of regular languages was introduced and studied in [O. Kupferman and J. Mosheiff, 2015], where the complexity of deciding the primality of the language of a given DFA was left open, with a doubly-exponential gap between the upper and lower bounds. We study primality for unary regular languages, namely regular languages with a singleton alphabet. A unary language corresponds to a subset of ℕ, making the study of unary prime languages closer to that of primality in number theory. We show that the setting of languages is richer. In particular, while every composite number is the product of two smaller numbers, the number t of languages necessary to decompose a composite unary language induces a strict hierarchy. In addition, a primality witness for a unary language L, namely a word that is not in L but is in all products of languages that contain L and have an index smaller than L’s, may be of exponential length. Still, we are able to characterize compositionality by structural properties of a DFA for L, leading to a LogSpace algorithm for primality checking of unary DFAs.},
author = {Jecker, Ismael R and Kupferman, Orna and Mazzocchi, Nicolas},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science},
isbn = {9783959771597},
issn = {18688969},
location = {Prague, Czech Republic},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Unary prime languages}},
doi = {10.4230/LIPIcs.MFCS.2020.51},
volume = {170},
year = {2020},
}
@inproceedings{8600,
abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
booktitle = {31st International Conference on Concurrency Theory},
isbn = {9783959771603},
issn = {18688969},
location = {Virtual},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Multi-dimensional long-run average problems for vector addition systems with states}},
doi = {10.4230/LIPIcs.CONCUR.2020.23},
volume = {171},
year = {2020},
}
@article{8671,
abstract = {We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space. },
author = {Shakiba, A. and Goharshady, Amir Kafshdar and Hooshmandasl, M.R. and Alambardar Meybodi, M.},
issn = {20089473},
journal = {Iranian Journal of Mathematical Sciences and Informatics},
number = {2},
pages = {117--128},
publisher = {ACECR Tarbiat Modares University},
title = {{A note on belief structures and s-approximation spaces}},
doi = {10.29252/ijmsi.15.2.117},
volume = {15},
year = {2020},
}
@article{8767,
abstract = {Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.},
author = {Kaveh, Kamran and McAvoy, Alex and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {1553-7358},
journal = {PLOS Computational Biology},
keywords = {Ecology, Modelling and Simulation, Computational Theory and Mathematics, Genetics, Ecology, Evolution, Behavior and Systematics, Molecular Biology, Cellular and Molecular Neuroscience},
number = {11},
publisher = {Public Library of Science},
title = {{The Moran process on 2-chromatic graphs}},
doi = {10.1371/journal.pcbi.1008402},
volume = {16},
year = {2020},
}
@article{8788,
abstract = {We consider a real-time setting where an environment releases sequences of firm-deadline tasks, and an online scheduler chooses on-the-fly the ones to execute on a single processor so as to maximize cumulated utility. The competitive ratio is a well-known performance measure for the scheduler: it gives the worst-case ratio, among all possible choices for the environment, of the cumulated utility of the online scheduler versus an offline scheduler that knows these choices in advance. Traditionally, competitive analysis is performed by hand, while automated techniques are rare and only handle static environments with independent tasks. We present a quantitative-verification framework for precedence-aware competitive analysis, where task releases may depend on preceding scheduling choices, i.e., the environment can respond to scheduling decisions dynamically . We consider two general classes of precedences: 1) follower precedences force the release of a dependent task upon the completion of a set of precursor tasks, while and 2) pairing precedences modify the characteristics of a dependent task provided the completion of a set of precursor tasks. Precedences make competitive analysis challenging, as the online and offline schedulers operate on diverging sequences. We make a formal presentation of our framework, and use a GPU-based implementation to analyze ten well-known schedulers on precedence-based application examples taken from the existing literature: 1) a handshake protocol (HP); 2) network packet-switching; 3) query scheduling (QS); and 4) a sporadic-interrupt setting. Our experimental results show that precedences and task parameters can vary drastically the best scheduler. Our framework thus supports application designers in choosing the best scheduler among a given set automatically.},
author = {Pavlogiannis, Andreas and Schaumberger, Nico and Schmid, Ulrich and Chatterjee, Krishnendu},
issn = {19374151},
journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems},
number = {11},
pages = {3981--3992},
publisher = {IEEE},
title = {{Precedence-aware automated competitive analysis of real-time scheduling}},
doi = {10.1109/TCAD.2020.3012803},
volume = {39},
year = {2020},
}
@article{8789,
abstract = {Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty.},
author = {Kleshnina, Maria and Streipert, Sabrina and Filar, Jerzy and Chatterjee, Krishnendu},
issn = {22277390},
journal = {Mathematics},
number = {11},
publisher = {MDPI},
title = {{Prioritised learning in snowdrift-type games}},
doi = {10.3390/math8111945},
volume = {8},
year = {2020},
}
@phdthesis{7196,
abstract = {In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.},
author = {Tkadlec, Josef},
issn = {2663-337X},
pages = {144},
publisher = {IST Austria},
title = {{A role of graphs in evolutionary processes}},
doi = {10.15479/AT:ISTA:7196},
year = {2020},
}
@article{7212,
abstract = {The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.},
author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {15537358},
journal = {PLoS computational biology},
publisher = {PLoS},
title = {{Limits on amplifiers of natural selection under death-Birth updating}},
doi = {10.1371/journal.pcbi.1007494},
volume = {16},
year = {2020},
}
@article{7343,
abstract = {Coinfections with multiple pathogens can result in complex within‐host dynamics affecting virulence and transmission. While multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collective disease defences of ants – their social immunity – influence pathogen competition in coinfections of same or different fungal pathogen species. Social immunity reduced virulence for all pathogen combinations, but interfered with spore production only in different‐species coinfections. Here, it decreased overall pathogen sporulation success while increasing co‐sporulation on individual cadavers and maintaining a higher pathogen diversity at the community level. Mathematical modelling revealed that host sanitary care alone can modulate competitive outcomes between pathogens, giving advantage to fast‐germinating, thus less grooming‐sensitive ones. Host social interactions can hence modulate infection dynamics in coinfected group members, thereby altering pathogen communities at the host level and population level.},
author = {Milutinovic, Barbara and Stock, Miriam and Grasse, Anna V and Naderlinger, Elisabeth and Hilbe, Christian and Cremer, Sylvia},
issn = {1461-023X},
journal = {Ecology Letters},
number = {3},
pages = {565--574},
publisher = {Wiley},
title = {{Social immunity modulates competition between coinfecting pathogens}},
doi = {10.1111/ele.13458},
volume = {23},
year = {2020},
}
@inproceedings{7346,
abstract = {The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature. },
author = {Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
booktitle = {Proceedings of the 23rd International Conference on Principles of Distributed Systems},
location = {Neuchâtel, Switzerland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{The evolutionary price of anarchy: Locally bounded agents in a dynamic virus game}},
doi = {10.4230/LIPIcs.OPODIS.2019.21},
volume = {153},
year = {2020},
}
@inproceedings{7955,
abstract = {Simple stochastic games are turn-based 2½-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a conjunction of such conditions as objective. Despite a plethora of recent results on the analysis of systems with multiple objectives, the decidability of this basic problem remains open. In this paper, we present an algorithm approximating the Pareto frontier of the achievable values to a given precision. Moreover, it is an anytime algorithm, meaning it can be stopped at any time returning the current approximation and its error bound.},
author = {Ashok, Pranav and Chatterjee, Krishnendu and Kretinsky, Jan and Weininger, Maximilian and Winkler, Tobias},
booktitle = {Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science },
isbn = {9781450371049},
location = {Saarbrücken, Germany},
pages = {102--115},
publisher = {Association for Computing Machinery},
title = {{Approximating values of generalized-reachability stochastic games}},
doi = {10.1145/3373718.3394761},
year = {2020},
}
@article{9197,
abstract = {In this paper we introduce and study all-pay bidding games, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn, each player submits a sealed legal bid (non-negative and below their remaining budget), which is deducted from their budget and the highest bidder moves the token onto an adjacent vertex. The game ends once a sink is reached, and Player 1 pays Player 2 the outcome that is associated with the sink. The players attempt to maximize their expected outcome. Our games model settings where effort (of no inherent value) needs to be invested in an ongoing and stateful manner. On the negative side, we show that even in simple games on DAGs, optimal strategies may require a distribution over bids with infinite support. A central quantity in bidding games is the ratio of the players budgets. On the positive side, we show a simple FPTAS for DAGs, that, for each budget ratio, outputs an approximation for the optimal strategy for that ratio. We also implement it, show that it performs well, and suggests interesting properties of these games. Then, given an outcome c, we show an algorithm for finding the necessary and sufficient initial ratio for guaranteeing outcome c with probability 1 and a strategy ensuring such. Finally, while the general case has not previously been studied, solving the specific game in which Player 1 wins iff he wins the first two auctions, has been long stated as an open question, which we solve.},
author = {Avni, Guy and Ibsen-Jensen, Rasmus and Tkadlec, Josef},
isbn = {978157735835-0},
issn = {2374-3468},
journal = {Proceedings of the AAAI Conference on Artificial Intelligence},
location = {New York, NY, United States},
number = {02},
pages = {1798--1805},
publisher = {Association for the Advancement of Artificial Intelligence},
title = {{All-pay bidding games on graphs}},
doi = {10.1609/aaai.v34i02.5546},
volume = {34},
year = {2020},
}
@inproceedings{7810,
abstract = {Interprocedural data-flow analyses form an expressive and useful paradigm of numerous static analysis applications, such as live variables analysis, alias analysis and null pointers analysis. The most widely-used framework for interprocedural data-flow analysis is IFDS, which encompasses distributive data-flow functions over a finite domain. On-demand data-flow analyses restrict the focus of the analysis on specific program locations and data facts. This setting provides a natural split between (i) an offline (or preprocessing) phase, where the program is partially analyzed and analysis summaries are created, and (ii) an online (or query) phase, where analysis queries arrive on demand and the summaries are used to speed up answering queries.
In this work, we consider on-demand IFDS analyses where the queries concern program locations of the same procedure (aka same-context queries). We exploit the fact that flow graphs of programs have low treewidth to develop faster algorithms that are space and time optimal for many common data-flow analyses, in both the preprocessing and the query phase. We also use treewidth to develop query solutions that are embarrassingly parallelizable, i.e. the total work for answering each query is split to a number of threads such that each thread performs only a constant amount of work. Finally, we implement a static analyzer based on our algorithms, and perform a series of on-demand analysis experiments on standard benchmarks. Our experimental results show a drastic speed-up of the queries after only a lightweight preprocessing phase, which significantly outperforms existing techniques.},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
booktitle = {European Symposium on Programming},
isbn = {9783030449131},
issn = {16113349},
location = {Dublin, Ireland},
pages = {112--140},
publisher = {Springer Nature},
title = {{Optimal and perfectly parallel algorithms for on-demand data-flow analysis}},
doi = {10.1007/978-3-030-44914-8_5},
volume = {12075},
year = {2020},
}
@inproceedings{8728,
abstract = {Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in O((n+m)⋅t2) time, given a tree decomposition of the MC with width t. Our results also imply a bound of O(κ⋅(n+m)⋅t2) for each objective on MDPs, where κ is the number of strategy-iteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on low-treewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experiments show that on low-treewidth MCs and MDPs, our algorithms outperform existing well-established methods by one or more orders of magnitude.},
author = {Asadi, Ali and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Mohammadi, Kiarash and Pavlogiannis, Andreas},
booktitle = {Automated Technology for Verification and Analysis},
isbn = {9783030591519},
issn = {0302-9743},
location = {Hanoi, Vietnam},
pages = {253--270},
publisher = {Springer Nature},
title = {{Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth}},
doi = {10.1007/978-3-030-59152-6_14},
volume = {12302},
year = {2020},
}
@inproceedings{8089,
abstract = {We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method based on positivstellensaetze, i.e. theorems in semi-algebraic geometry that characterize positive polynomials over a semi-algebraic set.
On the theoretical side, the worst-case complexity of our approach is subexponential, whereas the worst-case complexity of the previous complete method (Kapur, ACA 2004) is doubly-exponential. Even when restricted to linear invariants, the best previous complexity for complete invariant generation is exponential (Colon et al, CAV 2003). On the practical side, we reduce the invariant generation problem to quadratic programming (QCLP), which is a classical optimization problem with many industrial solvers. We demonstrate the applicability of our approach by providing experimental results on several academic benchmarks. To the best of our knowledge, the only previous invariant generation method that provides completeness guarantees for invariants consisting of polynomial inequalities is (Kapur, ACA 2004), which relies on quantifier elimination and cannot even handle toy programs such as our running example.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar and Goharshady, Ehsan Kafshdar},
booktitle = {Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation},
isbn = {9781450376136},
location = {London, United Kingdom},
pages = {672--687},
publisher = {Association for Computing Machinery},
title = {{Polynomial invariant generation for non-deterministic recursive programs}},
doi = {10.1145/3385412.3385969},
year = {2020},
}
@article{6918,
abstract = {We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard.
We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.},
author = {Goharshady, Amir Kafshdar and Mohammadi, Fatemeh},
issn = {09518320},
journal = {Reliability Engineering and System Safety},
publisher = {Elsevier},
title = {{An efficient algorithm for computing network reliability in small treewidth}},
doi = {10.1016/j.ress.2019.106665},
volume = {193},
year = {2020},
}
@inproceedings{7183,
abstract = {A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in Ω(n2).},
author = {Brázdil, Tomás and Chatterjee, Krishnendu and Kucera, Antonín and Novotný, Petr and Velan, Dominik},
booktitle = {International Symposium on Automated Technology for Verification and Analysis},
isbn = {9783030317836},
issn = {16113349},
location = {Taipei, Taiwan},
pages = {462--478},
publisher = {Springer Nature},
title = {{Deciding fast termination for probabilistic VASS with nondeterminism}},
doi = {10.1007/978-3-030-31784-3_27},
volume = {11781},
year = {2019},
}
@article{7210,
abstract = {The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these amplifiers of natural selection typically increase fixation time. Here we study population structures that achieve a tradeoff between fixation probability and time. First, we show that no amplifiers can have an asymptotically lower absorption time than the well-mixed population. Then we design population structures that substantially augment the fixation probability with just a minor increase in fixation time. Finally, we show that those structures enable higher effective rate of evolution than the well-mixed population provided that the rate of generating advantageous mutants is relatively low. Our work sheds light on how population structure affects the rate of evolution. Moreover, our structures could be useful for lab-based, medical, or industrial applications of evolutionary optimization.},
author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {2399-3642},
journal = {Communications Biology},
publisher = {Springer Nature},
title = {{Population structure determines the tradeoff between fixation probability and fixation time}},
doi = {10.1038/s42003-019-0373-y},
volume = {2},
year = {2019},
}
@inproceedings{7402,
abstract = {Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary, to represent the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. Consequently, our polynomial-time algorithm for adversarial stopping time also computes an optimal plan among all possible plans.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
booktitle = {34th Annual ACM/IEEE Symposium on Logic in Computer Science},
isbn = {9781728136080},
location = {Vancouver, BC, Canada},
pages = {1--13},
publisher = {IEEE},
title = {{Graph planning with expected finite horizon}},
doi = {10.1109/lics.2019.8785706},
year = {2019},
}
@unpublished{7950,
abstract = {The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:
1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.
2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.
3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.},
author = {Biniaz, Ahmad and Jain, Kshitij and Lubiw, Anna and Masárová, Zuzana and Miltzow, Tillmann and Mondal, Debajyoti and Naredla, Anurag Murty and Tkadlec, Josef and Turcotte, Alexi},
booktitle = {arXiv},
title = {{Token swapping on trees}},
year = {2019},
}
@inproceedings{5948,
abstract = {We study the termination problem for nondeterministic probabilistic programs. We consider the bounded termination problem that asks whether the supremum of the expected termination time over all schedulers is bounded. First, we show that ranking supermartingales (RSMs) are both sound and complete for proving bounded termination over nondeterministic probabilistic programs. For nondeterministic probabilistic programs a previous result claimed that RSMs are not complete for bounded termination, whereas our result corrects the previous flaw and establishes completeness with a rigorous proof. Second, we present the first sound approach to establish lower bounds on expected termination time through RSMs.},
author = {Fu, Hongfei and Chatterjee, Krishnendu},
booktitle = {International Conference on Verification, Model Checking, and Abstract Interpretation},
location = {Cascais, Portugal},
pages = {468--490},
publisher = {Springer Nature},
title = {{Termination of nondeterministic probabilistic programs}},
doi = {10.1007/978-3-030-11245-5_22},
volume = {11388},
year = {2019},
}
@inproceedings{6462,
abstract = {A controller is a device that interacts with a plant. At each time point,it reads the plant’s state and issues commands with the goal that the plant oper-ates optimally. Constructing optimal controllers is a fundamental and challengingproblem. Machine learning techniques have recently been successfully applied totrain controllers, yet they have limitations. Learned controllers are monolithic andhard to reason about. In particular, it is difficult to add features without retraining,to guarantee any level of performance, and to achieve acceptable performancewhen encountering untrained scenarios. These limitations can be addressed bydeploying quantitative run-timeshieldsthat serve as a proxy for the controller.At each time point, the shield reads the command issued by the controller andmay choose to alter it before passing it on to the plant. We show how optimalshields that interfere as little as possible while guaranteeing a desired level ofcontroller performance, can be generated systematically and automatically usingreactive synthesis. First, we abstract the plant by building a stochastic model.Second, we consider the learned controller to be a black box. Third, we mea-surecontroller performanceandshield interferenceby two quantitative run-timemeasures that are formally defined using weighted automata. Then, the problemof constructing a shield that guarantees maximal performance with minimal inter-ference is the problem of finding an optimal strategy in a stochastic2-player game“controller versus shield” played on the abstract state space of the plant with aquantitative objective obtained from combining the performance and interferencemeasures. We illustrate the effectiveness of our approach by automatically con-structing lightweight shields for learned traffic-light controllers in various roadnetworks. The shields we generate avoid liveness bugs, improve controller per-formance in untrained and changing traffic situations, and add features to learnedcontrollers, such as giving priority to emergency vehicles.},
author = {Avni, Guy and Bloem, Roderick and Chatterjee, Krishnendu and Henzinger, Thomas A and Konighofer, Bettina and Pranger, Stefan},
booktitle = {31st International Conference on Computer-Aided Verification},
isbn = {9783030255398},
issn = {0302-9743},
location = {New York, NY, United States},
pages = {630--649},
publisher = {Springer},
title = {{Run-time optimization for learned controllers through quantitative games}},
doi = {10.1007/978-3-030-25540-4_36},
volume = {11561},
year = {2019},
}
@article{6836,
abstract = {Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1,2,3,4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine cooperation and welfare7,8,9,10. Most previous models of reciprocity do not include inequality11,12,13,14,15. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.},
author = {Hauser, Oliver P. and Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin A.},
issn = {14764687},
journal = {Nature},
number = {7770},
pages = {524--527},
publisher = {Springer Nature},
title = {{Social dilemmas among unequals}},
doi = {10.1038/s41586-019-1488-5},
volume = {572},
year = {2019},
}
@inproceedings{6885,
abstract = {A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Long-run average behavior of vector addition systems with states}},
doi = {10.4230/LIPICS.CONCUR.2019.27},
volume = {140},
year = {2019},
}
@inproceedings{6887,
abstract = {The fundamental model-checking problem, given as input a model and a specification, asks for the algorithmic verification of whether the model satisfies the specification. Two classical models for reactive systems are graphs and Markov decision processes (MDPs). A basic specification formalism in the verification of reactive systems is the strong fairness (aka Streett) objective, where given different types of requests and corresponding grants, the requirement is that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All omega-regular objectives can be expressed as Streett objectives and hence they are canonical in verification. Consider graphs/MDPs with n vertices, m edges, and a Streett objectives with k pairs, and let b denote the size of the description of the Streett objective for the sets of requests and grants. The current best-known algorithm for the problem requires time O(min(n^2, m sqrt{m log n}) + b log n). In this work we present randomized near-linear time algorithms, with expected running time O~(m + b), where the O~ notation hides poly-log factors. Our randomized algorithms are near-linear in the size of the input, and hence optimal up to poly-log factors. },
author = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika and Svozil, Alexander},
booktitle = {Leibniz International Proceedings in Informatics},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Near-linear time algorithms for Streett objectives in graphs and MDPs}},
doi = {10.4230/LIPICS.CONCUR.2019.7},
volume = {140},
year = {2019},
}
@inproceedings{6889,
abstract = {We study Markov decision processes and turn-based stochastic games with parity conditions. There are three qualitative winning criteria, namely, sure winning, which requires all paths to satisfy the condition, almost-sure winning, which requires the condition to be satisfied with probability 1, and limit-sure winning, which requires the condition to be satisfied with probability arbitrarily close to 1. We study the combination of two of these criteria for parity conditions, e.g., there are two parity conditions one of which must be won surely, and the other almost-surely. The problem has been studied recently by Berthon et al. for MDPs with combination of sure and almost-sure winning, under infinite-memory strategies, and the problem has been established to be in NP cap co-NP. Even in MDPs there is a difference between finite-memory and infinite-memory strategies. Our main results for combination of sure and almost-sure winning are as follows: (a) we show that for MDPs with finite-memory strategies the problem is in NP cap co-NP; (b) we show that for turn-based stochastic games the problem is co-NP-complete, both for finite-memory and infinite-memory strategies; and (c) we present algorithmic results for the finite-memory case, both for MDPs and turn-based stochastic games, by reduction to non-stochastic parity games. In addition we show that all the above complexity results also carry over to combination of sure and limit-sure winning, and results for all other combinations can be derived from existing results in the literature. Thus we present a complete picture for the study of combinations of two qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games. },
author = {Chatterjee, Krishnendu and Piterman, Nir},
location = {Amsterdam, Netherlands},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Combinations of Qualitative Winning for Stochastic Parity Games}},
doi = {10.4230/LIPICS.CONCUR.2019.6},
volume = {140},
year = {2019},
}
@inproceedings{6942,
abstract = {Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of 𝜔 -regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.},
author = {Ashok, Pranav and Brázdil, Tomáš and Chatterjee, Krishnendu and Křetínský, Jan and Lampert, Christoph and Toman, Viktor},
booktitle = {16th International Conference on Quantitative Evaluation of Systems},
isbn = {9783030302801},
issn = {0302-9743},
location = {Glasgow, United Kingdom},
pages = {109--128},
publisher = {Springer Nature},
title = {{Strategy representation by decision trees with linear classifiers}},
doi = {10.1007/978-3-030-30281-8_7},
volume = {11785},
year = {2019},
}
@inproceedings{6884,
abstract = {In two-player games on graphs, the players move a token through a graph to produce a finite or infinite path, which determines the qualitative winner or quantitative payoff of the game. We study bidding games in which the players bid for the right to move the token. Several bidding rules were studied previously. In Richman bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Poorman bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. Taxman bidding spans the spectrum between Richman and poorman bidding. They are parameterized by a constant tau in [0,1]: portion tau of the winning bid is paid to the other player, and portion 1-tau to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games. It was previously shown that both Richman and poorman infinite-duration games with qualitative objectives reduce to reachability games, and we show a similar result here. Our most interesting results concern quantitative taxman games, namely mean-payoff games, where poorman and Richman bidding differ significantly. A central quantity in these games is the ratio between the two players' initial budgets. While in poorman mean-payoff games, the optimal payoff of a player depends on the initial ratio, in Richman bidding, the payoff depends only on the structure of the game. In both games the optimal payoffs can be found using (different) probabilistic connections with random-turn games in which in each turn, instead of bidding, a coin is tossed to determine which player moves. While the value with Richman bidding equals the value of a random-turn game with an un-biased coin, with poorman bidding, the bias in the coin is the initial ratio of the budgets. We give a complete classification of mean-payoff taxman games that is based on a probabilistic connection: the value of a taxman bidding game with parameter tau and initial ratio r, equals the value of a random-turn game that uses a coin with bias F(tau, r) = (r+tau * (1-r))/(1+tau). Thus, we show that Richman bidding is the exception; namely, for every tau <1, the value of the game depends on the initial ratio. Our proof technique simplifies and unifies the previous proof techniques for both Richman and poorman bidding. },
author = {Avni, Guy and Henzinger, Thomas A and Zikelic, Dorde},
location = {Aachen, Germany},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Bidding mechanisms in graph games}},
doi = {10.4230/LIPICS.MFCS.2019.11},
volume = {138},
year = {2019},
}
@article{7158,
abstract = {
Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, and so on. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth.
Our main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing but can answer subsequent queries significantly faster as compared to the current algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches.
},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goyal, Prateesh and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {0164-0925},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth}},
doi = {10.1145/3363525},
volume = {41},
year = {2019},
}
@article{7014,
abstract = {We study the problem of developing efficient approaches for proving
worst-case bounds of non-deterministic recursive programs. Ranking functions
are sound and complete for proving termination and worst-case bounds of
nonrecursive programs. First, we apply ranking functions to recursion,
resulting in measure functions. We show that measure functions provide a sound
and complete approach to prove worst-case bounds of non-deterministic recursive
programs. Our second contribution is the synthesis of measure functions in
nonpolynomial forms. We show that non-polynomial measure functions with
logarithm and exponentiation can be synthesized through abstraction of
logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem
using linear programming. While previous methods obtain worst-case polynomial
bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$
as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present
experimental results to demonstrate that our approach can obtain efficiently
worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the
divide-and-conquer algorithm for the Closest-Pair problem, where we obtain
$\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for
polynomial multiplication and Strassen's algorithm for matrix multiplication,
where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and
close to the best-known bounds for the respective algorithms.},
author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar},
journal = {ACM Transactions on Programming Languages and Systems},
number = {4},
publisher = {ACM},
title = {{Non-polynomial worst-case analysis of recursive programs}},
doi = {10.1145/3339984},
volume = {41},
year = {2019},
}
@inproceedings{6378,
abstract = {In today's cryptocurrencies, Hashcash proof of work is the most commonly-adopted approach to mining. In Hashcash, when a miner decides to add a block to the chain, she has to solve the difficult computational puzzle of inverting a hash function. While Hashcash has been successfully adopted in both Bitcoin and Ethereum, it has attracted significant and harsh criticism due to its massive waste of electricity, its carbon footprint and environmental effects, and the inherent lack of usefulness in inverting a hash function. Various other mining protocols have been suggested, including proof of stake, in which a miner's chance of adding the next block is proportional to her current balance. However, such protocols lead to a higher entry cost for new miners who might not still have any stake in the cryptocurrency, and can in the worst case lead to an oligopoly, where the rich have complete control over mining. In this paper, we propose Hybrid Mining: a new mining protocol that combines solving real-world useful problems with Hashcash. Our protocol allows new miners to join the network by taking part in Hashcash mining without having to own an initial stake. It also allows nodes of the network to submit hard computational problems whose solutions are of interest in the real world, e.g.~protein folding problems. Then, miners can choose to compete in solving these problems, in lieu of Hashcash, for adding a new block. Hence, Hybrid Mining incentivizes miners to solve useful problems, such as hard computational problems arising in biology, in a distributed manner. It also gives researchers in other areas an easy-to-use tool to outsource their hard computations to the blockchain network, which has enormous computational power, by paying a reward to the miner who solves the problem for them. Moreover, our protocol provides strong security guarantees and is at least as resilient to double spending as Bitcoin.},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Pourdamghani, Arash},
booktitle = {Proceedings of the 34th ACM Symposium on Applied Computing},
isbn = {9781450359337},
location = {Limassol, Cyprus},
pages = {374--381},
publisher = {ACM},
title = {{Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving}},
doi = {10.1145/3297280.3297319},
volume = {Part F147772},
year = {2019},
}
@inproceedings{6780,
abstract = {In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a
given probabilistic program terminates with probability 1. Scalable approaches for program analysis often
rely on modularity as their theoretical basis. In non-probabilistic programs, the classical variant rule (V-rule)
of Floyd-Hoare logic provides the foundation for modular analysis. Extension of this rule to almost-sure
termination of probabilistic programs is quite tricky, and a probabilistic variant was proposed in [16]. While the
proposed probabilistic variant cautiously addresses the key issue of integrability, we show that the proposed
modular rule is still not sound for almost-sure termination of probabilistic programs.
Besides establishing unsoundness of the previous rule, our contributions are as follows: First, we present a
sound modular rule for almost-sure termination of probabilistic programs. Our approach is based on a novel
notion of descent supermartingales. Second, for algorithmic approaches, we consider descent supermartingales
that are linear and show that they can be synthesized in polynomial time. Finally, we present experimental
results on a variety of benchmarks and several natural examples that model various types of nested while
loops in probabilistic programs and demonstrate that our approach is able to efficiently prove their almost-sure
termination property},
author = {Huang, Mingzhang and Fu, Hongfei and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar},
booktitle = {Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications },
location = {Athens, Greece},
publisher = {ACM},
title = {{Modular verification for almost-sure termination of probabilistic programs}},
doi = {10.1145/3360555},
volume = {3},
year = {2019},
}
@inproceedings{6175,
abstract = {We consider the problem of expected cost analysis over nondeterministic probabilistic programs,
which aims at automated methods for analyzing the resource-usage of such programs.
Previous approaches for this problem could only handle nonnegative bounded costs.
However, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols,
both positive and negative costs are necessary and the costs are unbounded as well.
In this work, we present a sound and efficient approach to obtain polynomial bounds on the
expected accumulated cost of nondeterministic probabilistic programs.
Our approach can handle (a) general positive and negative costs with bounded updates in
variables; and (b) nonnegative costs with general updates to variables.
We show that several natural examples which could not be
handled by previous approaches are captured in our framework.
Moreover, our approach leads to an efficient polynomial-time algorithm, while no
previous approach for cost analysis of probabilistic programs could guarantee polynomial runtime.
Finally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds.},
author = {Wang, Peixin and Fu, Hongfei and Goharshady, Amir Kafshdar and Chatterjee, Krishnendu and Qin, Xudong and Shi, Wenjun},
booktitle = {PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation},
keywords = {Program Cost Analysis, Program Termination, Probabilistic Programs, Martingales},
location = {Phoenix, AZ, United States},
pages = {204--220},
publisher = {Association for Computing Machinery},
title = {{Cost analysis of nondeterministic probabilistic programs}},
doi = {10.1145/3314221.3314581},
year = {2019},
}
@article{6380,
abstract = {There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: We show there is a number q* depending on the cache parameters such that (a) if the access hypergraph of order q* has constant treewidth, then there is a linear-time algorithm for Data Packing; (b)the Data Packing problem remains NP-hard even if the access hypergraph of order q*-1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q* of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses. },
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Okati, Nastaran and Pavlogiannis, Andreas},
issn = {2475-1421},
journal = {Proceedings of the ACM on Programming Languages},
number = {POPL},
publisher = {ACM},
title = {{Efficient parameterized algorithms for data packing}},
doi = {10.1145/3290366},
volume = {3},
year = {2019},
}
@inproceedings{6490,
abstract = {Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed by every node in the Blockchain network. Therefore, optimizations in compiling smart contracts can lead to significant savings in computation, time and energy.
Two classical approaches in program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, the analyses are usually reduced to graph problems over the control flow graph (CFG) of the program. These graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs for efficient algorithms. One such well-studied property is the treewidth, which is a measure of tree-likeness of graphs. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. This result has been used as a basis for many efficient intraprocedural analyses.
In this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case.
},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goharshady, Ehsan Kafshdar},
booktitle = {Proceedings of the 34th ACM Symposium on Applied Computing},
isbn = {9781450359337},
location = {Limassol, Cyprus},
pages = {400--408},
publisher = {ACM},
title = {{The treewidth of smart contracts}},
doi = {10.1145/3297280.3297322},
volume = {Part F147772},
year = {2019},
}
@inproceedings{6056,
abstract = {In today's programmable blockchains, smart contracts are limited to being deterministic and non-probabilistic. This lack of randomness is a consequential limitation, given that a wide variety of real-world financial contracts, such as casino games and lotteries, depend entirely on randomness. As a result, several ad-hoc random number generation approaches have been developed to be used in smart contracts. These include ideas such as using an oracle or relying on the block hash. However, these approaches are manipulatable, i.e. their output can be tampered with by parties who might not be neutral, such as the owner of the oracle or the miners.We propose a novel game-theoretic approach for generating provably unmanipulatable pseudorandom numbers on the blockchain. Our approach allows smart contracts to access a trustworthy source of randomness that does not rely on potentially compromised miners or oracles, hence enabling the creation of a new generation of smart contracts that are not limited to being non-probabilistic and can be drawn from the much more general class of probabilistic programs.},
author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Pourdamghani, Arash},
booktitle = {IEEE International Conference on Blockchain and Cryptocurrency},
location = {Seoul, Korea},
publisher = {IEEE},
title = {{Probabilistic smart contracts: Secure randomness on the blockchain}},
doi = {10.1109/BLOC.2019.8751326},
year = {2019},
}
@inproceedings{24,
abstract = {Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies that optimize the expectation of the discounted-sum payoff. A key drawback of the expectation measure is that even low probability events with extreme payoff can significantly affect the expectation, and thus the obtained policies are not necessarily risk-averse. An alternate approach is to optimize the probability that the payoff is above a certain threshold, which allows obtaining risk-averse policies, but ignores optimization of the expectation. We consider the expectation optimization with probabilistic guarantee (EOPG) problem, where the goal is to optimize the expectation ensuring that the payoff is above a given threshold with at least a specified probability. We present several results on the EOPG problem, including the first algorithm to solve it.},
author = {Chatterjee, Krishnendu and Elgyütt, Adrian and Novotny, Petr and Rouillé, Owen},
location = {Stockholm, Sweden},
pages = {4692 -- 4699},
publisher = {IJCAI},
title = {{Expectation optimization with probabilistic guarantees in POMDPs with discounted-sum objectives}},
doi = {10.24963/ijcai.2018/652},
volume = {2018},
year = {2018},
}
@inproceedings{25,
abstract = {Partially observable Markov decision processes (POMDPs) are the standard models for planning under uncertainty with both finite and infinite horizon. Besides the well-known discounted-sum objective, indefinite-horizon objective (aka Goal-POMDPs) is another classical objective for POMDPs. In this case, given a set of target states and a positive cost for each transition, the optimization objective is to minimize the expected total cost until a target state is reached. In the literature, RTDP-Bel or heuristic search value iteration (HSVI) have been used for solving Goal-POMDPs. Neither of these algorithms has theoretical convergence guarantees, and HSVI may even fail to terminate its trials. We give the following contributions: (1) We discuss the challenges introduced in Goal-POMDPs and illustrate how they prevent the original HSVI from converging. (2) We present a novel algorithm inspired by HSVI, termed Goal-HSVI, and show that our algorithm has convergence guarantees. (3) We show that Goal-HSVI outperforms RTDP-Bel on a set of well-known examples.},
author = {Horák, Karel and Bošanský, Branislav and Chatterjee, Krishnendu},
booktitle = {Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence},
location = {Stockholm, Sweden},
pages = {4764 -- 4770},
publisher = {IJCAI},
title = {{Goal-HSVI: Heuristic search value iteration for goal-POMDPs}},
doi = {10.24963/ijcai.2018/662},
volume = {2018-July},
year = {2018},
}
@article{293,
abstract = {People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple game theory model, which we call the signal-burying game. This game has the feature that senders can bury their signal by deliberately reducing the probability of the signal being observed. If the signal is observed, however, it is identified as having been buried. We show under which conditions buried signals can be maintained, using static equilibrium concepts and calculations of the evolutionary dynamics. We apply our analysis to shed light on a number of otherwise puzzling social phenomena, including modesty, anonymous donations, subtlety in art and fashion, and overeagerness.},
author = {Hoffman, Moshe and Hilbe, Christian and Nowak, Martin},
journal = {Nature Human Behaviour},
pages = {397 -- 404},
publisher = {Nature Publishing Group},
title = {{The signal-burying game can explain why we obscure positive traits and good deeds}},
doi = {10.1038/s41562-018-0354-z},
volume = {2},
year = {2018},
}
@inproceedings{297,
abstract = {Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with ω -regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropy-based techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.},
author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Kretinsky, Jan and Toman, Viktor},
location = {Thessaloniki, Greece},
pages = {385 -- 407},
publisher = {Springer},
title = {{Strategy representation by decision trees in reactive synthesis}},
doi = {10.1007/978-3-319-89960-2_21},
volume = {10805},
year = {2018},
}
@inbook{86,
abstract = {Responsiveness—the requirement that every request to a system be eventually handled—is one of the fundamental liveness properties of a reactive system. Average response time is a quantitative measure for the responsiveness requirement used commonly in performance evaluation. We show how average response time can be computed on state-transition graphs, on Markov chains, and on game graphs. In all three cases, we give polynomial-time algorithms.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
booktitle = {Principles of Modeling},
editor = {Lohstroh, Marten and Derler, Patricia and Sirjani, Marjan},
pages = {143 -- 161},
publisher = {Springer},
title = {{Computing average response time}},
doi = {10.1007/978-3-319-95246-8_9},
volume = {10760},
year = {2018},
}
@article{198,
abstract = {We consider a class of students learning a language from a teacher. The situation can be interpreted as a group of child learners receiving input from the linguistic environment. The teacher provides sample sentences. The students try to learn the grammar from the teacher. In addition to just listening to the teacher, the students can also communicate with each other. The students hold hypotheses about the grammar and change them if they receive counter evidence. The process stops when all students have converged to the correct grammar. We study how the time to convergence depends on the structure of the classroom by introducing and evaluating various complexity measures. We find that structured communication between students, although potentially introducing confusion, can greatly reduce some of the complexity measures. Our theory can also be interpreted as applying to the scientific process, where nature is the teacher and the scientists are the students.},
author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin},
journal = {Journal of the Royal Society Interface},
number = {140},
publisher = {Royal Society},
title = {{Language acquisition with communication between learners}},
doi = {10.1098/rsif.2018.0073},
volume = {15},
year = {2018},
}