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
IS - 1
JF - Discrete Applied Mathematics
SN - 0166218X
TI - Optimal strategies for selecting coordinators
VL - 289
ER -
TY - THES
AB - 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.
AU - Goharshady, Amir Kafshdar
ID - 8934
SN - 2663-337X
TI - Parameterized and algebro-geometric advances in static program analysis
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Karkhanis, Deep
AU - Novotný, Petr
AU - Royer, Amélie
ID - 8193
SN - 23340835
T2 - Proceedings of the 30th International Conference on Automated Planning and Scheduling
TI - Multiple-environment Markov decision processes: Efficient analysis and applications
VL - 30
ER -
TY - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Katoen, Joost P
AU - Weininger, Maximilian
AU - Winkler, Tobias
ID - 8272
SN - 03029743
T2 - International Conference on Computer Aided Verification
TI - Stochastic games with lexicographic reachability-safety objectives
VL - 12225
ER -
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 - CONF
AB - 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.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 8600
SN - 18688969
T2 - 31st International Conference on Concurrency Theory
TI - Multi-dimensional long-run average problems for vector addition systems with states
VL - 171
ER -
TY - JOUR
AB - We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space.
AU - Shakiba, A.
AU - Goharshady, Amir Kafshdar
AU - Hooshmandasl, M.R.
AU - Alambardar Meybodi, M.
ID - 8671
IS - 2
JF - Iranian Journal of Mathematical Sciences and Informatics
SN - 17354463
TI - A note on belief structures and s-approximation spaces
VL - 15
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 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 -