TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Jecker, Ismael R
AU - Svoboda, Jakub
ID - 8533
SN - 18688969
T2 - 45th International Symposium on Mathematical Foundations of Computer Science
TI - Simplified game of life: Algorithms and complexity
VL - 170
ER -
TY - CONF
AB - 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.
AU - Jecker, Ismael R
AU - Kupferman, Orna
AU - Mazzocchi, Nicolas
ID - 8534
SN - 18688969
T2 - 45th International Symposium on Mathematical Foundations of Computer Science
TI - Unary prime languages
VL - 170
ER -
TY - JOUR
AB - 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.
AU - Kaveh, Kamran
AU - McAvoy, Alex
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 8767
IS - 11
JF - PLOS Computational Biology
KW - Ecology
KW - Modelling and Simulation
KW - Computational Theory and Mathematics
KW - Genetics
KW - Ecology
KW - Evolution
KW - Behavior and Systematics
KW - Molecular Biology
KW - Cellular and Molecular Neuroscience
SN - 1553-734X
TI - The Moran process on 2-chromatic graphs
VL - 16
ER -
TY - JOUR
AB - 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.
AU - Goharshady, Amir Kafshdar
AU - Mohammadi, Fatemeh
ID - 6918
JF - Reliability Engineering and System Safety
SN - 09518320
TI - An efficient algorithm for computing network reliability in small treewidth
VL - 193
ER -
TY - JOUR
AB - 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.
AU - Milutinovic, Barbara
AU - Stock, Miriam
AU - Grasse, Anna V
AU - Naderlinger, Elisabeth
AU - Hilbe, Christian
AU - Cremer, Sylvia
ID - 7343
IS - 3
JF - Ecology Letters
SN - 1461-023X
TI - Social immunity modulates competition between coinfecting pathogens
VL - 23
ER -
TY - JOUR
AB - 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.
AU - Kleshnina, Maria
AU - Streipert, Sabrina
AU - Filar, Jerzy
AU - Chatterjee, Krishnendu
ID - 8789
IS - 11
JF - Mathematics
TI - Prioritised learning in snowdrift-type games
VL - 8
ER -
TY - JOUR
AB - 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.
AU - Zeiner, Martin
AU - Schmid, Ulrich
AU - Chatterjee, Krishnendu
ID - 8793
JF - Discrete Applied Mathematics
SN - 0166218X
TI - Optimal strategies for selecting coordinators
ER -
TY - CONF
AB - 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.
AU - Ashok, Pranav
AU - Chatterjee, Krishnendu
AU - Kretinsky, Jan
AU - Weininger, Maximilian
AU - Winkler, Tobias
ID - 7955
SN - 9781450371049
T2 - Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Approximating values of generalized-reachability stochastic games
ER -
TY - JOUR
AB - 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.
AU - Pavlogiannis, Andreas
AU - Schaumberger, Nico
AU - Schmid, Ulrich
AU - Chatterjee, Krishnendu
ID - 8788
IS - 11
JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
SN - 02780070
TI - Precedence-aware automated competitive analysis of real-time scheduling
VL - 39
ER -
TY - CONF
AB - 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).
AU - Brázdil, Tomás
AU - Chatterjee, Krishnendu
AU - Kucera, Antonín
AU - Novotný, Petr
AU - Velan, Dominik
ID - 7183
SN - 03029743
T2 - International Symposium on Automated Technology for Verification and Analysis
TI - Deciding fast termination for probabilistic VASS with nondeterminism
VL - 11781
ER -
TY - JOUR
AB - 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.
AU - Tkadlec, Josef
AU - Pavlogiannis, Andreas
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 7210
JF - Communications Biology
SN - 2399-3642
TI - Population structure determines the tradeoff between fixation probability and fixation time
VL - 2
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 7402
SN - 9781728136080
T2 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Graph planning with expected finite horizon
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Pourdamghani, Arash
ID - 6056
T2 - IEEE International Conference on Blockchain and Cryptocurrency
TI - Probabilistic smart contracts: Secure randomness on the blockchain
ER -
TY - CONF
AB - 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.
AU - Wang, Peixin
AU - Fu, Hongfei
AU - Goharshady, Amir Kafshdar
AU - Chatterjee, Krishnendu
AU - Qin, Xudong
AU - Shi, Wenjun
ID - 6175
KW - Program Cost Analysis
KW - Program Termination
KW - Probabilistic Programs
KW - Martingales
T2 - PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation
TI - Cost analysis of nondeterministic probabilistic programs
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Pourdamghani, Arash
ID - 6378
SN - 9781450359337
T2 - Proceedings of the 34th ACM Symposium on Applied Computing
TI - Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving
VL - Part F147772
ER -
TY - JOUR
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Okati, Nastaran
AU - Pavlogiannis, Andreas
ID - 6380
IS - POPL
JF - Proceedings of the ACM on Programming Languages
SN - 2475-1421
TI - Efficient parameterized algorithms for data packing
VL - 3
ER -
TY - CONF
AB - 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.
AU - Avni, Guy
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Konighofer, Bettina
AU - Pranger, Stefan
ID - 6462
SN - 0302-9743
T2 - 31st International Conference on Computer-Aided Verification
TI - Run-time optimization for learned controllers through quantitative games
VL - 11561
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Goharshady, Ehsan Kafshdar
ID - 6490
SN - 9781450359337
T2 - Proceedings of the 34th ACM Symposium on Applied Computing
TI - The treewidth of smart contracts
VL - Part F147772
ER -
TY - CONF
AB - 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
AU - Huang, Mingzhang
AU - Fu, Hongfei
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
ID - 6780
T2 - Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications
TI - Modular verification for almost-sure termination of probabilistic programs
VL - 3
ER -
TY - JOUR
AB - 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.
AU - Hauser, Oliver P.
AU - Hilbe, Christian
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 6836
IS - 7770
JF - Nature
SN - 00280836
TI - Social dilemmas among unequals
VL - 572
ER -
TY - CONF
AB - 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.
AU - Avni, Guy
AU - Henzinger, Thomas A
AU - Zikelic, Dorde
ID - 6884
TI - Bidding mechanisms in graph games
VL - 138
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 6885
TI - Long-run average behavior of vector addition systems with states
VL - 140
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Svozil, Alexander
ID - 6887
T2 - Leibniz International Proceedings in Informatics
TI - Near-linear time algorithms for Streett objectives in graphs and MDPs
VL - 140
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Piterman, Nir
ID - 6889
TI - Combinations of Qualitative Winning for Stochastic Parity Games
VL - 140
ER -
TY - CONF
AB - 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.
AU - Ashok, Pranav
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Křetínský, Jan
AU - Lampert, Christoph
AU - Toman, Viktor
ID - 6942
SN - 0302-9743
T2 - 16th International Conference on Quantitative Evaluation of Systems
TI - Strategy representation by decision trees with linear classifiers
VL - 11785
ER -
TY - JOUR
AB - 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.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir Kafshdar
ID - 7014
IS - 4
JF - ACM Transactions on Programming Languages and Systems
TI - Non-polynomial worst-case analysis of recursive programs
VL - 41
ER -
TY - JOUR
AB -
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.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir Kafshdar
AU - Goyal, Prateesh
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 7158
IS - 4
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth
VL - 41
ER -
TY - CONF
AB - 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.
AU - Fu, Hongfei
AU - Chatterjee, Krishnendu
ID - 5948
T2 - International Conference on Verification, Model Checking, and Abstract Interpretation
TI - Termination of nondeterministic probabilistic programs
VL - 11388
ER -
TY - GEN
AB - 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.
AU - Biniaz, Ahmad
AU - Jain, Kshitij
AU - Lubiw, Anna
AU - Masárová, Zuzana
AU - Miltzow, Tillmann
AU - Mondal, Debajyoti
AU - Naredla, Anurag Murty
AU - Tkadlec, Josef
AU - Turcotte, Alexi
ID - 7950
T2 - arXiv
TI - Token swapping on trees
ER -
TY - JOUR
AB - Indirect reciprocity explores how humans act when their reputation is at stake, and which social norms they use to assess the actions of others. A crucial question in indirect reciprocity is which social norms can maintain stable cooperation in a society. Past research has highlighted eight such norms, called “leading-eight” strategies. This past research, however, is based on the assumption that all relevant information about other population members is publicly available and that everyone agrees on who is good or bad. Instead, here we explore the reputation dynamics when information is private and noisy. We show that under these conditions, most leading-eight strategies fail to evolve. Those leading-eight strategies that do evolve are unable to sustain full cooperation.Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other’s reputation, previous research has highlighted eight crucial moral systems. These “leading-eight” strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.
AU - Hilbe, Christian
AU - Schmid, Laura
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 2
IS - 48
JF - PNAS
TI - Indirect reciprocity with private, noisy, and incomplete information
VL - 115
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Elgyütt, Adrian
AU - Novotny, Petr
AU - Rouillé, Owen
ID - 24
TI - Expectation optimization with probabilistic guarantees in POMDPs with discounted-sum objectives
VL - 2018
ER -
TY - JOUR
AB - This paper is devoted to automatic competitive analysis of real-time scheduling algorithms for firm-deadline tasksets, where only completed tasks con- tribute some utility to the system. Given such a taskset T , the competitive ratio of an on-line scheduling algorithm A for T is the worst-case utility ratio of A over the utility achieved by a clairvoyant algorithm. We leverage the theory of quantitative graph games to address the competitive analysis and competitive synthesis problems. For the competitive analysis case, given any taskset T and any finite-memory on- line scheduling algorithm A , we show that the competitive ratio of A in T can be computed in polynomial time in the size of the state space of A . Our approach is flexible as it also provides ways to model meaningful constraints on the released task sequences that determine the competitive ratio. We provide an experimental study of many well-known on-line scheduling algorithms, which demonstrates the feasibility of our competitive analysis approach that effectively replaces human ingenuity (required Preliminary versions of this paper have appeared in Chatterjee et al. ( 2013 , 2014 ). B Andreas Pavlogiannis pavlogiannis@ist.ac.at Krishnendu Chatterjee krish.chat@ist.ac.at Alexander Kößler koe@ecs.tuwien.ac.at Ulrich Schmid s@ecs.tuwien.ac.at 1 IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria 2 Embedded Computing Systems Group, Vienna University of Technology, Treitlstrasse 3, 1040 Vienna, Austria 123 Real-Time Syst for finding worst-case scenarios) by computing power. For the competitive synthesis case, we are just given a taskset T , and the goal is to automatically synthesize an opti- mal on-line scheduling algorithm A , i.e., one that guarantees the largest competitive ratio possible for T . We show how the competitive synthesis problem can be reduced to a two-player graph game with partial information, and establish that the compu- tational complexity of solving this game is Np -complete. The competitive synthesis problem is hence in Np in the size of the state space of the non-deterministic labeled transition system encoding the taskset. Overall, the proposed framework assists in the selection of suitable scheduling algorithms for a given taskset, which is in fact the most common situation in real-time systems design.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 738
IS - 1
JF - Real-Time Systems
TI - Automated competitive analysis of real time scheduling with graph games
VL - 54
ER -
TY - CONF
AB - Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.
AU - Arming, Sebastian
AU - Bartocci, Ezio
AU - Chatterjee, Krishnendu
AU - Katoen, Joost P
AU - Sokolova, Ana
ID - 79
TI - Parameter-independent strategies for pMDPs via POMDPs
VL - 11024
ER -
TY - JOUR
AB - Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution.
AU - Hilbe, Christian
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 419
JF - Nature Human Behaviour
TI - Partners and rivals in direct reciprocity
VL - 2
ER -
TY - JOUR
AB - Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect on each other. Here we introduce a general framework that allows us to analyze “crosstalk” between a player’s concurrent games. In the presence of crosstalk, the action a person experiences in one game can alter the person’s decision in another. We find that crosstalk impedes the maintenance of cooperation and requires stronger levels of forgiveness. The magnitude of the effect depends on the population structure. In more densely connected social groups, crosstalk has a stronger effect. A harsh retaliator, such as Tit-for-Tat, is unable to counteract crosstalk. The crosstalk framework provides a unified interpretation of direct and upstream reciprocity in the context of repeated games.
AU - Reiter, Johannes
AU - Hilbe, Christian
AU - Rand, David
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 454
IS - 1
JF - Nature Communications
TI - Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness
VL - 9
ER -
TY - CONF
AB - We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.
AU - Huang, Mingzhang
AU - Fu, Hongfei
AU - Chatterjee, Krishnendu
ED - Ryu, Sukyoung
ID - 5679
SN - 03029743
TI - New approaches for almost-sure termination of probabilistic programs
VL - 11275
ER -
TY - JOUR
AB - Because of the intrinsic randomness of the evolutionary process, a mutant with a fitness advantage has some chance to be selected but no certainty. Any experiment that searches for advantageous mutants will lose many of them due to random drift. It is therefore of great interest to find population structures that improve the odds of advantageous mutants. Such structures are called amplifiers of natural selection: they increase the probability that advantageous mutants are selected. Arbitrarily strong amplifiers guarantee the selection of advantageous mutants, even for very small fitness advantage. Despite intensive research over the past decade, arbitrarily strong amplifiers have remained rare. Here we show how to construct a large variety of them. Our amplifiers are so simple that they could be useful in biotechnology, when optimizing biological molecules, or as a diagnostic tool, when searching for faster dividing cells or viruses. They could also occur in natural population structures.
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin A.
ID - 5751
IS - 1
JF - Communications Biology
SN - 2399-3642
TI - Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory
VL - 1
ER -
TY - CHAP
AB - Graph-based games are an important tool in computer science. They have applications in synthesis, verification, refinement, and far beyond. We review graphbased games with objectives on infinite plays. We give definitions and algorithms to solve the games and to give a winning strategy. The objectives we consider are mostly Boolean, but we also look at quantitative graph-based games and their objectives. Synthesis aims to turn temporal logic specifications into correct reactive systems. We explain the reduction of synthesis to graph-based games (or equivalently tree automata) using synthesis of LTL specifications as an example. We treat the classical approach that uses determinization of parity automata and more modern approaches.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Jobstmann, Barbara
ED - Henzinger, Thomas A
ED - Clarke, Edmund M.
ED - Veith, Helmut
ED - Bloem, Roderick
ID - 59
SN - 978-3-319-10574-1
T2 - Handbook of Model Checking
TI - Graph games and reactive synthesis
ER -
TY - CONF
AB - The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.
Blackwell and Ferguson (1968) give an ε-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. We prove that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient.
AU - Hansen, Kristoffer Arnsfelt
AU - Ibsen-Jensen, Rasmus
AU - Neyman, Abraham
ID - 5967
SN - 9781450358293
T2 - Proceedings of the 2018 ACM Conference on Economics and Computation - EC '18
TI - The Big Match with a clock and a bit of memory
ER -
TY - CONF
AB - We consider the stochastic shortest path (SSP)problem for succinct Markov decision processes(MDPs), where the MDP consists of a set of vari-ables, and a set of nondeterministic rules that up-date the variables. First, we show that several ex-amples from the AI literature can be modeled assuccinct MDPs. Then we present computationalapproaches for upper and lower bounds for theSSP problem: (a) for computing upper bounds, ourmethod is polynomial-time in the implicit descrip-tion of the MDP; (b) for lower bounds, we present apolynomial-time (in the size of the implicit descrip-tion) reduction to quadratic programming. Our ap-proach is applicable even to infinite-state MDPs.Finally, we present experimental results to demon-strate the effectiveness of our approach on severalclassical examples from the AI literature.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir
AU - Okati, Nastaran
ID - 5977
SN - 10450823
T2 - Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
TI - Computational approaches for stochastic shortest path on succinct MDPs
VL - 2018
ER -
TY - JOUR
AB - In this article, we consider the termination problem of probabilistic programs with real-valued variables. Thequestions concerned are: qualitative ones that ask (i) whether the program terminates with probability 1(almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); andquantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) tocompute a boundBsuch that the probability not to terminate afterBsteps decreases exponentially (con-centration problem). To solve these questions, we utilize the notion of ranking supermartingales, which isa powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmicsynthesis of linear ranking-supermartingales over affine probabilistic programs (Apps) with both angelic anddemonic non-determinism. An important subclass of Apps is LRApp which is defined as the class of all Appsover which a linear ranking-supermartingale exists.Our main contributions are as follows. Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor Apps with angelic non-determinism. Moreover, theNP-hardness result holds already for Appswithout probability and demonic non-determinism. Secondly, we show that the concentration problem overLRApp can be solved in the same complexity as for the membership problem of LRApp. Finally, we show thatthe expectation problem over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate theeffectiveness of our approach to answer the qualitative and quantitative questions over Apps with at mostdemonic non-determinism.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Novotný, Petr
AU - Hasheminezhad, Rouzbeh
ID - 5993
IS - 2
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs
VL - 40
ER -
TY - JOUR
AB - We study algorithmic questions wrt algebraic path properties in concurrent systems, where the transitions of the system are labeled from a complete, closed semiring. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time.
Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Goharshady, Amir Kafshdar
AU - Pavlogiannis, Andreas
ID - 6009
IS - 3
JF - ACM Transactions on Programming Languages and Systems
SN - 0164-0925
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
VL - 40
ER -
TY - JOUR
AB - 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.
AU - Hoffman, Moshe
AU - Hilbe, Christian
AU - Nowak, Martin
ID - 293
JF - Nature Human Behaviour
TI - The signal-burying game can explain why we obscure positive traits and good deeds
VL - 2
ER -
TY - CONF
AB - 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.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Kretinsky, Jan
AU - Toman, Viktor
ID - 297
TI - Strategy representation by decision trees in reactive synthesis
VL - 10805
ER -
TY - CONF
AB - A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to the standard RAM operations. We give lower bounds on the number of symbolic operations for basic graph problems such as the computation of the strongly connected components and of the approximate diameter as well as for fundamental problems in model checking such as safety, liveness, and coliveness. Our lower bounds are linear in the number of vertices of the graph, even for constant-diameter graphs. For none of these problems lower bounds on the number of symbolic operations were known before. The lower bounds show an interesting separation of these problems from the reachability problem, which can be solved with O(D) symbolic operations, where D is the diameter of the graph. Additionally we present an approximation algorithm for the graph diameter which requires Õ(n/D) symbolic steps to achieve a (1 +ϵ)-approximation for any constant > 0. This compares to O(n/D) symbolic steps for the (naive) exact algorithm and O(D) symbolic steps for a 2-approximation. Finally we also give a refined analysis of the strongly connected components algorithms of [15], showing that it uses an optimal number of symbolic steps that is proportional to the sum of the diameters of the strongly connected components.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 310
TI - Lower bounds for symbolic computation on graphs: Strongly connected components, liveness, safety and diameter
ER -
TY - CONF
AB - Smart contracts are computer programs that are executed by a network of mutually distrusting agents, without the need of an external trusted authority. Smart contracts handle and transfer assets of considerable value (in the form of crypto-currency like Bitcoin). Hence, it is crucial that their implementation is bug-free. We identify the utility (or expected payoff) of interacting with such smart contracts as the basic and canonical quantitative property for such contracts. We present a framework for such quantitative analysis of smart contracts. Such a formal framework poses new and novel research challenges in programming languages, as it requires modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior and modeling utilities which are not specified as standard temporal properties such as safety and termination. While game-theoretic incentives have been analyzed in the security community, their analysis has been restricted to the very special case of stateless games. However, to analyze smart contracts, stateful analysis is required as it must account for the different program states of the protocol. Our main contributions are as follows: we present (i)~a simplified programming language for smart contracts; (ii)~an automatic translation of the programs to state-based games; (iii)~an abstraction-refinement approach to solve such games; and (iv)~experimental results on real-world-inspired smart contracts.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Velner, Yaron
ID - 311
TI - Quantitative analysis of smart contracts
VL - 10801
ER -
TY - CONF
AB - We present a secure approach for maintaining andreporting credit history records on the Blockchain. Our ap-proach removes third-parties such as credit reporting agen-cies from the lending process and replaces them with smartcontracts. This allows customers to interact directly with thelenders or banks while ensuring the integrity, unmalleabilityand privacy of their credit data. Additionally, each customerhas full control over complete or selective disclosure of hercredit records, eliminating the risk of privacy violations or databreaches. Moreover, our approach provides strong guaranteesfor the lenders as well. A lender can check both correctness andcompleteness of the credit data disclosed to her. This is the firstapproach that can perform all credit reporting tasks withouta central authority or changing the financial mechanisms*.
AU - Goharshady, Amir Kafshdar
AU - Behrouz, Ali
AU - Chatterjee, Krishnendu
ID - 6340
SN - 978-1-5386-7975-3
T2 - Proceedings of the IEEE International Conference on Blockchain
TI - Secure Credit Reporting on the Blockchain
ER -
TY - CONF
AB - Crypto-currencies are digital assets designed to work as a medium of exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest behavior of participants). A framework for the analysis of attacks in crypto-currencies requires (a) modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior; (b) concurrent interactions between participants; and (c) analysis of long-term monetary gains. Traditional game-theoretic approaches for the analysis of security protocols consider either qualitative temporal properties such as safety and termination, or the very special class of one-shot (stateless) games. However, to analyze general attacks on protocols for crypto-currencies, both stateful analysis and quantitative objectives are necessary. In this work our main contributions are as follows: (a) we show how a class of concurrent mean-payo games, namely ergodic games, can model various attacks that arise naturally in crypto-currencies; (b) we present the first practical implementation of algorithms for ergodic games that scales to model realistic problems for crypto-currencies; and (c) we present experimental results showing that our framework can handle games with thousands of states and millions of transitions.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Ibsen-Jensen, Rasmus
AU - Velner, Yaron
ID - 66
SN - 978-3-95977-087-3
TI - Ergodic mean-payoff games for the analysis of attacks in crypto-currencies.
VL - 118
ER -
TY - JOUR
AB - Social dilemmas occur when incentives for individuals are misaligned with group interests 1-7 . According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment - either naturally occurring or designed - help to overcome social dilemmas.
AU - Hilbe, Christian
AU - Šimsa, Štepán
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 157
IS - 7713
JF - Nature
TI - Evolution of cooperation in stochastic games
VL - 559
ER -
TY - JOUR
AB - 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.
AU - Ibsen-Jensen, Rasmus
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 198
IS - 140
JF - Journal of the Royal Society Interface
TI - Language acquisition with communication between learners
VL - 15
ER -