@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},
}