TY - CONF
AB - We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. 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 where there are k different target sets, and the problems are as follows: (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 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 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) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Svozil, Alexander
ID - 35
T2 - 28th International Conference on Automated Planning and Scheduling
TI - Algorithms and conditional lower bounds for planning problems
ER -
TY - CONF
AB - Partially observable Markov decision processes (POMDPs) are the standard models for planning under uncertainty with both finite and infinite horizon. Besides the well-known discounted-sum objective, indefinite-horizon objective (aka Goal-POMDPs) is another classical objective for POMDPs. In this case, given a set of target states and a positive cost for each transition, the optimization objective is to minimize the expected total cost until a target state is reached. In the literature, RTDP-Bel or heuristic search value iteration (HSVI) have been used for solving Goal-POMDPs. Neither of these algorithms has theoretical convergence guarantees, and HSVI may even fail to terminate its trials. We give the following contributions: (1) We discuss the challenges introduced in Goal-POMDPs and illustrate how they prevent the original HSVI from converging. (2) We present a novel algorithm inspired by HSVI, termed Goal-HSVI, and show that our algorithm has convergence guarantees. (3) We show that Goal-HSVI outperforms RTDP-Bel on a set of well-known examples.
AU - Horák, Karel
AU - Bošanský, Branislav
AU - Chatterjee, Krishnendu
ID - 25
T2 - Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
TI - Goal-HSVI: Heuristic search value iteration for goal-POMDPs
VL - 2018-July
ER -
TY - JOUR
AB - Two-player games on graphs are central in many problems in formal verification and program analysis, such as synthesis and verification of open systems. In this work, we consider solving recursive game graphs (or pushdown game graphs) that model the control flow of sequential programs with recursion.While pushdown games have been studied before with qualitative objectives-such as reachability and ?-regular objectives- in this work, we study for the first time such games with the most well-studied quantitative objective, the mean-payoff objective. In pushdown games, two types of strategies are relevant: (1) global strategies, which depend on the entire global history; and (2) modular strategies, which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity by showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games and memoryless modular strategies are sufficient in two-player pushdown games. Finally, we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 716
IS - 5
JF - Journal of the ACM
SN - 00045411
TI - The complexity of mean-payoff pushdown games
VL - 64
ER -
TY - JOUR
AB - We consider finite-state and recursive game graphs with multidimensional mean-payoff objectives. In recursive games two types of strategies are relevant: global strategies and modular strategies. Our contributions are: (1) We show that finite-state multidimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of weights are fixed; whereas for arbitrary dimensions the problem is coNP-complete. (2) We show that one-player recursive games with multidimensional mean-payoff objectives can be solved in polynomial time. Both above algorithms are based on hyperplane separation technique. (3) For recursive games we show that under modular strategies the multidimensional problem is undecidable. We show that if the number of modules, exits, and the maximal absolute value of the weights are fixed, then one-dimensional recursive mean-payoff games under modular strategies can be solved in polynomial time, whereas for unbounded number of exits or modules the problem is NP-hard.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 717
JF - Journal of Computer and System Sciences
TI - Hyperplane separation technique for multidimensional mean-payoff games
VL - 88
ER -
TY - JOUR
AB - The ubiquity of computation in modern machines and devices imposes a need to assert the correctness of their behavior. Especially in the case of safety-critical systems, their designers need to take measures that enforce their safe operation. Formal methods has emerged as a research field that addresses this challenge: by rigorously proving that all system executions adhere to their specifications, the correctness of an implementation under concern can be assured. To achieve this goal, a plethora of techniques are nowadays available, all of which are optimized for different system types and application domains.
AU - Chatterjee, Krishnendu
AU - Ehlers, Rüdiger
ID - 719
IS - 6
JF - Acta Informatica
SN - 00015903
TI - Special issue: Synthesis and SYNT 2014
VL - 54
ER -
TY - JOUR
AB - In evolutionary game theory interactions between individuals are often assumed obligatory. However, in many real-life situations, individuals can decide to opt out of an interaction depending on the information they have about the opponent. We consider a simple evolutionary game theoretic model to study such a scenario, where at each encounter between two individuals the type of the opponent (cooperator/defector) is known with some probability, and where each individual either accepts or opts out of the interaction. If the type of the opponent is unknown, a trustful individual accepts the interaction, whereas a suspicious individual opts out of the interaction. If either of the two individuals opt out both individuals remain without an interaction. We show that in the prisoners dilemma optional interactions along with suspicious behaviour facilitates the emergence of trustful cooperation.
AU - Priklopil, Tadeas
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 744
JF - Journal of Theoretical Biology
SN - 00225193
TI - Optional interactions and suspicious behaviour facilitates trustful cooperation in prisoners dilemma
VL - 433
ER -
TY - JOUR
AB - The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on n vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time O(n5/2) and for (2) k-pair Streett objectives in graphs in time O(n2+nklogn). For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 464
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Improved algorithms for parity and Streett objectives
VL - 13
ER -
TY - JOUR
AB - The edit distance between two words w 1 , w 2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w 1 to w 2 . The edit distance generalizes to languages L 1 , L 2 , where the edit distance from L 1 to L 2 is the minimal number k such that for every word from L 1 there exists a word in L 2 with edit distance at most k . We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for the following problems: (1) deciding whether, for a given threshold k , the edit distance from a pushdown automaton to a finite automaton is at most k , and (2) deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 465
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Edit distance for pushdown automata
VL - 13
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Křetínská, Zuzana
AU - Kretinsky, Jan
ID - 466
IS - 2
JF - Logical Methods in Computer Science
SN - 18605974
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
VL - 13
ER -
TY - JOUR
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata or in any other known decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata, which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in runtime verification. We establish an almost-complete decidability picture for the basic decision problems about nested weighted automata and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 467
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
SN - 15293785
TI - Nested weighted automata
VL - 18
ER -
TY - JOUR
AB - The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Cometswarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 512
IS - 1
JF - Scientific Reports
SN - 20452322
TI - Amplification on undirected population structures: Comets beat stars
VL - 7
ER -
TY - GEN
AB - A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graphwhere the edges are labeled with different types of opening and closing parentheses, and the reachabilityinformation is computed via paths whose parentheses are properly matched. We present new results for Dyckreachability problems with applications to alias analysis and data-dependence analysis. Our main contributions,that include improved upper bounds as well as lower bounds that establish optimality guarantees, are asfollows:First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing field-sensitive points-to analysis. Given a bidirected graph withnnodes andmedges, we present: (i) an algorithmwith worst-case running timeO(m+n·α(n)), whereα(n)is the inverse Ackermann function, improving thepreviously knownO(n2)time bound; (ii) a matching lower bound that shows that our algorithm is optimalwrt to worst-case complexity; and (iii) an optimal average-case upper bound ofO(m)time, improving thepreviously knownO(m·logn)bound.Second, we consider the problem of context-sensitive data-dependence analysis, where the task is to obtainanalysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almostlinear time, after which the contribution of the library in the complexity of the client analysis is only linear,and only wrt the number of call sites.Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly sub-cubic bounds cannot be obtained without obtaining sub-cubic combinatorial algorithms for Boolean MatrixMultiplication, which is a long-standing open problem. Thus we establish that the existing combinatorialalgorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the samehardness holds for graphs of constant treewidth.Finally, we provide a prototype implementation of our algorithms for both alias analysis and data-dependenceanalysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform allexisting methods on the two problems, over real-world benchmarks.
AU - Chatterjee, Krishnendu
AU - Choudhary, Bhavya
AU - Pavlogiannis, Andreas
ID - 5455
SN - 2664-1690
TI - Optimal Dyck reachability for data-dependence and alias analysis
ER -
TY - GEN
AB - We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class.
We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence.
1. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence.
2. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence.
Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes.
AU - Chalupa, Marek
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Sinha, Nishant
AU - Vaidya, Kapil
ID - 5456
SN - 2664-1690
TI - Data-centric dynamic partial order reduction
ER -
TY - CONF
AB - Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider the classical birth-death Moran process where there are two types of individuals, namely, the residents with fitness 1 and mutants with fitness r. The fitness indicates the reproductive strength. The evolutionary dynamics happens as follows: in the initial step, in a population of all resident individuals a mutant is introduced, and then at each step, an individual is chosen proportional to the fitness of its type to reproduce, and the offspring replaces a neighbor uniformly at random. The process stops when all individuals are either residents or mutants. The probability that all individuals in the end are mutants is called the fixation probability, which is a key factor in the rate of evolution. We consider the problem of approximating the fixation probability. The class of algorithms that is extremely relevant for approximation of the fixation probabilities is the Monte-Carlo simulation of the process. Previous results present a polynomial-time Monte-Carlo algorithm for undirected graphs when r is given in unary. First, we present a simple modification: instead of simulating each step, we discard ineffective steps, where no node changes type (i.e., either residents replace residents, or mutants replace mutants). Using the above simple modification and our result that the number of effective steps is concentrated around the expected number of effective steps, we present faster polynomial-time Monte-Carlo algorithms for undirected graphs. Our algorithms are always at least a factor O(n2/ log n) faster as compared to the previous algorithms, where n is the number of nodes, and is polynomial even if r is given in binary. We also present lower bounds showing that the upper bound on the expected number of effective steps we present is asymptotically tight for undirected graphs.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 551
SN - 978-395977046-0
T2 - Leibniz International Proceedings in Informatics
TI - Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs
VL - 83
ER -
TY - CONF
AB - Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first player is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). There are two variants of the problem, namely, the threshold problem where the quantitative goal is to ensure that the mean-payoff value is above a threshold, and the value problem where the quantitative goal is to ensure the optimal mean-payoff value; in both cases ensuring the qualitative parity objective. The previous best-known algorithms for game graphs with n vertices, m edges, parity objectives with d priorities, and maximal absolute reward value W for mean-payoff objectives, are as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for the value problem. Our main contributions are faster algorithms, and the running times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem, and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives with two priorities, our algorithms match the best-known bounds of the algorithms for mean-payoff games (without conjunction with parity objectives). Our results are relevant in synthesis of reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective).
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Svozil, Alexander
ID - 552
SN - 978-395977046-0
T2 - Leibniz International Proceedings in Informatics
TI - Faster algorithms for mean payoff parity games
VL - 83
ER -
TY - CONF
AB - We consider two player, zero-sum, finite-state concurrent reachability games, played for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. Player 1 wins iff a designated goal state is eventually visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed. Our main results are as follows: We show that: (i) the optimal bound on the patience of optimal and -optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary.
AU - Chatterjee, Krishnendu
AU - Hansen, Kristofer
AU - Ibsen-Jensen, Rasmus
ID - 553
SN - 978-395977046-0
T2 - Leibniz International Proceedings in Informatics
TI - Strategy complexity of concurrent safety games
VL - 83
ER -
TY - DATA
AB - Strong amplifiers of natural selection
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak , Martin
ID - 5559
KW - natural selection
TI - Strong amplifiers of natural selection
ER -
TY - CHAP
AB - In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision problems for classical quantitative objectives, such as sum, discounted sum, energy, and mean-payoff for two standard models of reactive systems, namely, graphs and graph games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ED - Aceto, Luca
ED - Bacci, Giorgio
ED - Ingólfsdóttir, Anna
ED - Legay, Axel
ED - Mardare, Radu
ID - 625
SN - 03029743
T2 - Models, Algorithms, Logics and Tools
TI - The cost of exactness in quantitative reachability
VL - 10460
ER -
TY - CONF
AB - We consider the problem of developing automated techniques for solving recurrence relations to aid the expected-runtime analysis of programs. The motivation is that several classical textbook algorithms have quite efficient expected-runtime complexity, whereas the corresponding worst-case bounds are either inefficient (e.g., Quick-Sort), or completely ineffective (e.g., Coupon-Collector). Since the main focus of expected-runtime analysis is to obtain efficient bounds, we consider bounds that are either logarithmic, linear or almost-linear (O(log n), O(n), O(n · log n), respectively, where n represents the input size). Our main contribution is an efficient (simple linear-time algorithm) sound approach for deriving such expected-runtime bounds for the analysis of recurrence relations induced by randomized algorithms. The experimental results show that our approach can efficiently derive asymptotically optimal expected-runtime bounds for recurrences of classical randomized algorithms, including Randomized-Search, Quick-Sort, Quick-Select, Coupon-Collector, where the worst-case bounds are either inefficient (such as linear as compared to logarithmic expected-runtime complexity, or quadratic as compared to linear or almost-linear expected-runtime complexity), or ineffective.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Murhekar, Aniket
ED - Majumdar, Rupak
ED - Kunčak, Viktor
ID - 628
SN - 978-331963386-2
TI - Automated recurrence analysis for almost linear expected runtime bounds
VL - 10426
ER -
TY - CONF
AB - Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks.
AU - Ashok, Pranav
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Kretinsky, Jan
AU - Meggendorfer, Tobias
ED - Majumdar, Rupak
ED - Kunčak, Viktor
ID - 645
SN - 978-331963386-2
TI - Value iteration for long run average reward in markov decision processes
VL - 10426
ER -
TY - CONF
AB - Graph games with omega-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the verification of branching time properties). Parity conditions are canonical forms to specify omega-regular winning conditions. Graph games with parity conditions are equivalent to mu-calculus model checking, and thus a very important algorithmic problem. Symbolic algorithms are of great significance because they provide scalable algorithms for the analysis of large finite-state systems, as well as algorithms for the analysis of infinite-state systems with finite quotient. A set-based symbolic algorithm uses the basic set operations and the one-step predecessor operators. We consider graph games with n vertices and parity conditions with c priorities (equivalently, a mu-calculus formula with c alternations of least and greatest fixed points). While many explicit algorithms exist for graph games with parity conditions, for set-based symbolic algorithms there are only two algorithms (notice that we use space to refer to the number of sets stored by a symbolic algorithm): (a) the basic algorithm that requires O(n^c) symbolic operations and linear space; and (b) an improved algorithm that requires O(n^{c/2+1}) symbolic operations but also O(n^{c/2+1}) space (i.e., exponential space). In this work we present two set-based symbolic algorithms for parity games: (a) our first algorithm requires O(n^{c/2+1}) symbolic operations and only requires linear space; and (b) developing on our first algorithm, we present an algorithm that requires O(n^{c/3+1}) symbolic operations and only linear space. We also present the first linear space set-based symbolic algorithm for parity games that requires at most a sub-exponential number of symbolic operations.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 6519
TI - Improved set-based symbolic algorithms for parity games
VL - 82
ER -
TY - JOUR
AB - The extent of heterogeneity among driver gene mutations present in naturally occurring metastases - that is, treatment-naive metastatic disease - is largely unknown. To address this issue, we carried out 60× whole-genome sequencing of 26 metastases from four patients with pancreatic cancer. We found that identical mutations in known driver genes were present in every metastatic lesion for each patient studied. Passenger gene mutations, which do not have known or predicted functional consequences, accounted for all intratumoral heterogeneity. Even with respect to these passenger mutations, our analysis suggests that the genetic similarity among the founding cells of metastases was higher than that expected for any two cells randomly taken from a normal tissue. The uniformity of known driver gene mutations among metastases in the same patient has critical and encouraging implications for the success of future targeted therapies in advanced-stage disease.
AU - Makohon Moore, Alvin
AU - Zhang, Ming
AU - Reiter, Johannes
AU - Božić, Ivana
AU - Allen, Benjamin
AU - Kundu, Deepanjan
AU - Chatterjee, Krishnendu
AU - Wong, Fay
AU - Jiao, Yuchen
AU - Kohutek, Zachary
AU - Hong, Jungeui
AU - Attiyeh, Marc
AU - Javier, Breanna
AU - Wood, Laura
AU - Hruban, Ralph
AU - Nowak, Martin
AU - Papadopoulos, Nickolas
AU - Kinzler, Kenneth
AU - Vogelstein, Bert
AU - Iacobuzio Donahue, Christine
ID - 653
IS - 3
JF - Nature Genetics
SN - 10614036
TI - Limited heterogeneity of known driver gene mutations among the metastases of individual patients with pancreatic cancer
VL - 49
ER -
TY - JOUR
AB - Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win-Stay Lose-Shift rule as a special case. A comprehensive numerical analysis for the prisoner's dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation.
AU - Hilbe, Christian
AU - Martinez, Vaquero
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 671
IS - 18
JF - PNAS
SN - 00278424
TI - Memory-n strategies of direct reciprocity
VL - 114
ER -
TY - JOUR
AB - Two-player games on graphs provide the theoretical framework for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of equilibria, they are decidable only for perfect-information games, whereas several applications require imperfect-information. In this paper we propose a new notion of equilibria, called doomsday equilibria, which is a strategy profile where all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players' objective, then the objective of every player is violated. We present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of ω-regular objectives, both for imperfect-information games, and for perfect-information games. We provide optimal complexity bounds for imperfect-information games, and in most cases for perfect-information games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Filiot, Emmanuel
AU - Raskin, Jean
ID - 681
JF - Information and Computation
SN - 08905401
TI - Doomsday equilibria for omega-regular games
VL - 254
ER -
TY - JOUR
AB - We generalize winning conditions in two-player games by adding a structural acceptance condition called obligations. Obligations are orthogonal to the linear winning conditions that define whether a play is winning. Obligations are a declaration that player 0 can achieve a certain value from a configuration. If the obligation is met, the value of that configuration for player 0 is 1. We define the value in such games and show that obligation games are determined. For Markov chains with Borel objectives and obligations, and finite turn-based stochastic parity games with obligations we give an alternative and simpler characterization of the value function. Based on this simpler definition we show that the decision problem of winning finite turn-based stochastic parity games with obligations is in NP∩co-NP. We also show that obligation games provide a game framework for reasoning about p-automata. © 2017 The Association for Symbolic Logic.
AU - Chatterjee, Krishnendu
AU - Piterman, Nir
ID - 684
IS - 2
JF - Journal of Symbolic Logic
SN - Obligation blackwell games and p-automata
TI - Obligation blackwell games and p-automata
VL - 82
ER -
TY - JOUR
AB - In antagonistic symbioses, such as host–parasite interactions, one population’s success is the other’s loss. In mutualistic symbioses, such as division of labor, both parties can gain, but they might have different preferences over the possible mutualistic arrangements. The rates of evolution of the two populations in a symbiosis are important determinants of which population will be more successful: Faster evolution is thought to be favored in antagonistic symbioses (the “Red Queen effect”), but disfavored in certain mutualistic symbioses (the “Red King effect”). However, it remains unclear which biological parameters drive these effects. Here, we analyze the effects of the various determinants of evolutionary rate: generation time, mutation rate, population size, and the intensity of natural selection. Our main results hold for the case where mutation is infrequent. Slower evolution causes a long-term advantage in an important class of mutualistic interactions. Surprisingly, less intense selection is the strongest driver of this Red King effect, whereas relative mutation rates and generation times have little effect. In antagonistic interactions, faster evolution by any means is beneficial. Our results provide insight into the demographic evolution of symbionts.
AU - Veller, Carl
AU - Hayward, Laura
AU - Nowak, Martin
AU - Hilbe, Christian
ID - 699
IS - 27
JF - PNAS
SN - 00278424
TI - The red queen and king in finite populations
VL - 114
ER -
TY - CONF
AB - Nested weighted automata (NWA) present a robust and convenient automata-theoretic formalism for quantitative specifications. Previous works have considered NWA that processed input words only in the forward direction. It is natural to allow the automata to process input words backwards as well, for example, to measure the maximal or average time between a response and the preceding request. We therefore introduce and study bidirectional NWA that can process input words in both directions. First, we show that bidirectional NWA can express interesting quantitative properties that are not expressible by forward-only NWA. Second, for the fundamental decision problems of emptiness and universality, we establish decidability and complexity results for the new framework which match the best-known results for the special case of forward-only NWA. Thus, for NWA, the increased expressiveness of bidirectionality is achieved at no additional computational complexity. This is in stark contrast to the unweighted case, where bidirectional finite automata are no more expressive but exponentially more succinct than their forward-only counterparts.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 711
SN - 18688969
TI - Bidirectional nested weighted automata
VL - 85
ER -
TY - THES
AB - This dissertation focuses on algorithmic aspects of program verification, and presents modeling and complexity advances on several problems related to the
static analysis of programs, the stateless model checking of concurrent programs, and the competitive analysis of real-time scheduling algorithms.
Our contributions can be broadly grouped into five categories.
Our first contribution is a set of new algorithms and data structures for the quantitative and data-flow analysis of programs, based on the graph-theoretic notion of treewidth.
It has been observed that the control-flow graphs of typical programs have special structure, and are characterized as graphs of small treewidth.
We utilize this structural property to provide faster algorithms for the quantitative and data-flow analysis of recursive and concurrent programs.
In most cases we make an algebraic treatment of the considered problem,
where several interesting analyses, such as the reachability, shortest path, and certain kind of data-flow analysis problems follow as special cases.
We exploit the constant-treewidth property to obtain algorithmic improvements for on-demand versions of the problems,
and provide data structures with various tradeoffs between the resources spent in the preprocessing and querying phase.
We also improve on the algorithmic complexity of quantitative problems outside the algebraic path framework,
namely of the minimum mean-payoff, minimum ratio, and minimum initial credit for energy problems.
Our second contribution is a set of algorithms for Dyck reachability with applications to data-dependence analysis and alias analysis.
In particular, we develop an optimal algorithm for Dyck reachability on bidirected graphs, which are ubiquitous in context-insensitive, field-sensitive points-to analysis.
Additionally, we develop an efficient algorithm for context-sensitive data-dependence analysis via Dyck reachability,
where the task is to obtain analysis summaries of library code in the presence of callbacks.
Our algorithm preprocesses libraries in almost linear time, after which the contribution of the library in the complexity of the client analysis is (i)~linear in the number of call sites and (ii)~only logarithmic in the size of the whole library, as opposed to linear in the size of the whole library.
Finally, we prove that Dyck reachability is Boolean Matrix Multiplication-hard in general, and the hardness also holds for graphs of constant treewidth.
This hardness result strongly indicates that there exist no combinatorial algorithms for Dyck reachability with truly subcubic complexity.
Our third contribution is the formalization and algorithmic treatment of the Quantitative Interprocedural Analysis framework.
In this framework, the transitions of a recursive program are annotated as good, bad or neutral, and receive a weight which measures
the magnitude of their respective effect.
The Quantitative Interprocedural Analysis problem asks to determine whether there exists an infinite run of the program where the long-run ratio of the bad weights over the good weights is above a given threshold.
We illustrate how several quantitative problems related to static analysis of recursive programs can be instantiated in this framework,
and present some case studies to this direction.
Our fourth contribution is a new dynamic partial-order reduction for the stateless model checking of concurrent programs. Traditional approaches rely on the standard Mazurkiewicz equivalence between traces, by means of partitioning the trace space into equivalence classes, and attempting to explore a few representatives from each class.
We present a new dynamic partial-order reduction method called the Data-centric Partial Order Reduction (DC-DPOR).
Our algorithm is based on a new equivalence between traces, called the observation equivalence.
DC-DPOR explores a coarser partitioning of the trace space than any exploration method based on the standard Mazurkiewicz equivalence.
Depending on the program, the new partitioning can be even exponentially coarser.
Additionally, DC-DPOR spends only polynomial time in each explored class.
Our fifth contribution is the use of automata and game-theoretic verification techniques in the competitive analysis and synthesis of real-time scheduling algorithms for firm-deadline tasks.
On the analysis side, we leverage automata on infinite words to compute the competitive ratio of real-time schedulers subject to various environmental constraints.
On the synthesis side, we introduce a new instance of two-player mean-payoff partial-information games, and show
how the synthesis of an optimal real-time scheduler can be reduced to computing winning strategies in this new type of games.
AU - Pavlogiannis, Andreas
ID - 821
TI - Algorithmic advances in program analysis and their applications
ER -
TY - CONF
AB - The notion of treewidth of graphs has been exploited for faster algorithms for several problems arising in verification and program analysis. Moreover, various notions of balanced tree decompositions have been used for improved algorithms supporting dynamic updates and analysis of concurrent programs. In this work, we present a tool for constructing tree-decompositions of CFGs obtained from Java methods, which is implemented as an extension to the widely used Soot framework. The experimental results show that our implementation on real-world Java benchmarks is very efficient. Our tool also provides the first implementation for balancing tree-decompositions. In summary, we present the first tool support for exploiting treewidth in the static analysis problems on Java programs.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Pavlogiannis, Andreas
ED - D'Souza, Deepak
ID - 949
SN - 03029743
TI - JTDec: A tool for tree decompositions in soot
VL - 10482
ER -
TY - CONF
AB - Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to $1$. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games. There, a central question is the existence and computation of threshold budgets; namely, a value t\in [0,1] such that if\PO's budget exceeds $t$, he can win the game, and if\PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games.
AU - Avni, Guy
AU - Henzinger, Thomas A
AU - Chonev, Ventsislav K
ID - 950
SN - 1868-8969
TI - Infinite-duration bidding games
VL - 85
ER -
TY - CONF
AB - Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.
AU - Chatterjee, Krishnendu
AU - Novotny, Petr
AU - Zikelic, Djordje
ID - 1194
IS - 1
SN - 07308566
TI - Stochastic invariants for probabilistic termination
VL - 52
ER -
TY - JOUR
AB - We study controller synthesis problems for finite-state Markov decision processes, where the objective is to optimize the expected mean-payoff performance and stability (also known as variability in the literature). We argue that the basic notion of expressing the stability using the statistical variance of the mean payoff is sometimes insufficient, and propose an alternative definition. We show that a strategy ensuring both the expected mean payoff and the variance below given bounds requires randomization and memory, under both the above definitions. We then show that the problem of finding such a strategy can be expressed as a set of constraints.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 1294
JF - Journal of Computer and System Sciences
TI - Trading performance for stability in Markov decision processes
VL - 84
ER -
TY - JOUR
AB - We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.
AU - Svoreňová, Mária
AU - Kretinsky, Jan
AU - Chmelik, Martin
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1407
IS - 2
JF - Nonlinear Analysis: Hybrid Systems
TI - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
VL - 23
ER -
TY - CONF
AB - A standard objective in partially-observable Markov decision processes (POMDPs) is to find a policy that maximizes the expected discounted-sum payoff. However, such policies may still permit unlikely but highly undesirable outcomes, which is problematic especially in safety-critical applications. Recently, there has been a surge of interest in POMDPs where the goal is to maximize the probability to ensure that the payoff is at least a given threshold, but these approaches do not consider any optimization beyond satisfying this threshold constraint. In this work we go beyond both the “expectation” and “threshold” approaches and consider a “guaranteed payoff optimization (GPO)” problem for POMDPs, where we are given a threshold t and the objective is to find a policy σ such that a) each possible outcome of σ yields a discounted-sum payoff of at least t, and b) the expected discounted-sum payoff of σ is optimal (or near-optimal) among all policies satisfying a). We present a practical approach to tackle the GPO problem and evaluate it on standard POMDP benchmarks.
AU - Chatterjee, Krishnendu
AU - Novotny, Petr
AU - Pérez, Guillermo
AU - Raskin, Jean
AU - Zikelic, Djordje
ID - 1009
T2 - Proceedings of the 31st AAAI Conference on Artificial Intelligence
TI - Optimizing expectation with guarantees in POMDPs
VL - 5
ER -
TY - CONF
AB - Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b) specify many natural parameters for algorithmic analysis, e.g., the number of entries and exits. We consider a general framework where RSM transitions are labeled from a semiring and path properties are algebraic with semiring operations, which can model, e.g., interprocedural reachability and dataflow analysis problems. Our main contributions are new algorithms for several fundamental problems. As compared to a direct translation of RSMs to PDSs and the best-known existing bounds of PDSs, our analysis algorithm improves the complexity for finite-height semirings (that subsumes reachability and standard dataflow properties). We further consider the problem of extracting distance values from the representation structures computed by our algorithm, and give efficient algorithms that distinguish the complexity of a one-time preprocessing from the complexity of each individual query. Another advantage of our algorithm is that our improvements carry over to the concurrent setting, where we improve the bestknown complexity for the context-bounded analysis of concurrent RSMs. Finally, we provide a prototype implementation that gives a significant speed-up on several benchmarks from the SLAM/SDV project.
AU - Chatterjee, Krishnendu
AU - Kragl, Bernhard
AU - Mishra, Samarth
AU - Pavlogiannis, Andreas
ED - Yang, Hongseok
ID - 1011
SN - 03029743
TI - Faster algorithms for weighted recursive state machines
VL - 10201
ER -
TY - JOUR
AB - We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs.
AU - Chatterjee, Krishnendu
AU - Osang, Georg F
ID - 1065
JF - Information Processing Letters
SN - 00200190
TI - Pushdown reachability with constant treewidth
VL - 122
ER -
TY - JOUR
AB - Simulation is an attractive alternative to language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. Simulation has also been extended in two orthogonal directions, namely, (1) fair simulation, for simulation over specified set of infinite runs; and (2) quantitative simulation, for simulation between weighted automata. While fair trace inclusion is PSPACE-complete, fair simulation can be computed in polynomial time. For weighted automata, the (quantitative) language inclusion problem is undecidable in general, whereas the (quantitative) simulation reduces to quantitative games, which admit pseudo-polynomial time algorithms.
In this work, we study (quantitative) simulation for weighted automata with Büchi acceptance conditions, i.e., we generalize fair simulation from non-weighted automata to weighted automata. We show that imposing Büchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games, yet they still admit pseudo-polynomial time algorithms.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Velner, Yaron
ID - 1066
IS - 2
JF - Information and Computation
TI - Quantitative fair simulation games
VL - 254
ER -
TY - JOUR
AB - Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic methods to accurately dissect subclones and their phylogenies from noisy and impure bulk tumour samples at unprecedented depth. However, existing methods are not designed to infer metastatic seeding patterns. Here we develop a tool, called Treeomics, to reconstruct the phylogeny of metastases and map subclones to their anatomic locations. Treeomics infers comprehensive seeding patterns for pancreatic, ovarian, and prostate cancers. Moreover, Treeomics correctly disambiguates true seeding patterns from sequencing artifacts; 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumour heterogeneity among distinct samples. In silico benchmarking on simulated tumour phylogenies across a wide range of sample purities (15–95%) and sequencing depths (25-800 × ) demonstrates the accuracy of Treeomics compared with existing methods.
AU - Reiter, Johannes
AU - Makohon Moore, Alvin
AU - Gerold, Jeffrey
AU - Božić, Ivana
AU - Chatterjee, Krishnendu
AU - Iacobuzio Donahue, Christine
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 1080
JF - Nature Communications
SN - 20411723
TI - Reconstructing metastatic seeding patterns of human cancers
VL - 8
ER -
TY - CONF
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 non-recursive programs. First, we apply ranking functions to recursion, resulting in measure functions, and show that they 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 non-polynomial 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 O(n log n) as well as O(nr) where r is not an integer. We present experimental results to demonstrate that our approach can efficiently obtain worst-case bounds of classical recursive algorithms such as Merge-Sort, Closest-Pair, Karatsuba’s algorithm and Strassen’s algorithm.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir
ED - Majumdar, Rupak
ED - Kunčak, Viktor
ID - 639
SN - 978-331963389-3
TI - Non-polynomial worst case analysis of recursive programs
VL - 10427
ER -
TY - CONF
AB - Magic: the Gathering is a game about magical combat for any number of players. Formally it is a zero-sum, imperfect information stochastic game that consists of a potentially unbounded number of steps. We consider the problem of deciding if a move is legal in a given single step of Magic. We show that the problem is (a) coNP-complete in general; and (b) in P if either of two small sets of cards are not used. Our lower bound holds even for single-player Magic games. The significant aspects of our results are as follows: First, in most real-life game problems, the task of deciding whether a given move is legal in a single step is trivial, and the computationally hard task is to find the best sequence of legal moves in the presence of multiple players. In contrast, quite uniquely our hardness result holds for single step and with only one-player. Second, we establish efficient algorithms for important special cases of Magic.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 478
TI - The complexity of deciding legality of a single step of magic: The gathering
VL - 285
ER -
TY - CONF
AB - Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph are controlled by two adversarial players, and the other transitions are executed probabilistically. We consider such games where the objective is the conjunction of several quantitative objectives (specified as mean-payoff conditions), which we refer to as generalized mean-payoff objectives. The basic decision problem asks for the existence of a finite-memory strategy for a player that ensures the generalized mean-payoff objective be satisfied with a desired probability against all strategies of the opponent. A special case of the decision problem is the almost-sure problem where the desired probability is 1. Previous results presented a semi-decision procedure for -approximations of the almost-sure problem. In this work, we show that both the almost-sure problem as well as the general basic decision problem are coNP-complete, significantly improving the previous results. Moreover, we show that in the case of 1-player stochastic games, randomized memoryless strategies are sufficient and the problem can be solved in polynomial time. In contrast, in two-player stochastic games, we show that even with randomized strategies exponential memory is required in general, and present a matching exponential upper bound. We also study the basic decision problem with infinite-memory strategies and present computational complexity results for the problem. Our results are relevant in the synthesis of stochastic reactive systems with multiple quantitative requirements.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 480
TI - Perfect-information stochastic games with generalized mean-payoff objectives
VL - 05-08-July-2016
ER -
TY - GEN
AB - We consider the quantitative analysis problem for interprocedural control-flow graphs (ICFGs). The input consists of an ICFG, a positive weight function that assigns every transition a positive integer-valued number, and a labelling of the transitions (events) as good, bad, and neutral events. The weight function assigns to each transition a numerical value that represents ameasure of how good or bad an event is. The quantitative analysis problem asks whether there is a run of the ICFG where the ratio of the sum of the numerical weights of good events versus the sum of weights of bad events in the long-run is at least a given threshold (or equivalently, to compute the maximal ratio among all valid paths in the ICFG). The quantitative analysis problem for ICFGs can be solved in polynomial time, and we present an efficient and practical algorithm for the problem. We show that several problems relevant for static program analysis, such as estimating the worst-case execution time of a program or the average energy consumption of a mobile application, can be modeled in our framework. We have implemented our algorithm as a tool in the Java Soot framework. We demonstrate the effectiveness of our approach with two case studies. First, we show that our framework provides a sound approach (no false positives) for the analysis of inefficiently-used containers. Second, we show that our approach can also be used for static profiling of programs which reasons about methods that are frequently invoked. Our experimental results show that our tool scales to relatively large benchmarks, and discovers relevant and useful information that can be used to optimize performance of the programs.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Velner, Yaron
ID - 5445
SN - 2664-1690
TI - Quantitative interprocedural analysis
ER -
TY - GEN
AB - The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population.
The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure.
Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade.
In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5449
SN - 2664-1690
TI - Amplification on undirected population structures: Comets beat stars
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5451
SN - 2664-1690
TI - Strong amplifiers of natural selection
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5452
SN - 2664-1690
TI - Arbitrarily strong amplifiers of natural selection
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5453
SN - 2664-1690
TI - Arbitrarily strong amplifiers of natural selection
ER -
TY - CONF
AB - Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decisionmaking and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning probability for a distinguished player, has received a lot of attention. Previous works consider the problem where the pairwise winning probabilities are known precisely, while we study how robust is the winning probability with respect to small errors in the pairwise winning probabilities. First, we present several illuminating examples to establish: (a) there exist deterministic tournaments (where the pairwise winning probabilities are 0 or 1) where one optimal draw is much more robust than the other; and (b) in general, there exist tournaments with slightly suboptimal draws that are more robust than all the optimal draws. The above examples motivate the study of the computational problem of robust draws that guarantee a specified winning probability. Second, we present a polynomial-time algorithm for approximating the robustness of a draw for sufficiently small errors in pairwise winning probabilities, and obtain that the stated computational problem is NP-complete. We also show that two natural cases of deterministic tournaments where the optimal draw could be computed in polynomial time also admit polynomial-time algorithms to compute robust optimal draws.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Tkadlec, Josef
ID - 1182
TI - Robust draws in balanced knockout tournaments
VL - 2016-January
ER -
TY - JOUR
AU - Hilbe, Christian
AU - Traulsen, Arne
ID - 1200
JF - Physics of Life Reviews
TI - Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze
VL - 19
ER -
TY - CONF
AB - To facilitate collaboration in massive online classrooms, instructors must make many decisions. For instance, the following parameters need to be decided when designing a peer-feedback system where students review each others' essays: the number of students each student must provide feedback to, an algorithm to map feedback providers to receivers, constraints that ensure students do not become free-riders (receiving feedback but not providing it), the best times to receive feedback to improve learning etc. While instructors can answer these questions by running experiments or invoking past experience, game-theoretic models with data from online learning platforms can identify better initial designs for further improvements. As an example, we explore the design space of a peer feedback system by modeling it using game theory. Our simulations show that incentivizing students to provide feedback requires the value obtained from receiving a feedback to exceed the cost of providing it by a large factor (greater than 7). Furthermore, hiding feedback from low-effort students incentivizes them to provide more feedback.
AU - Pandey, Vineet
AU - Chatterjee, Krishnendu
ID - 1245
IS - Februar-2016
T2 - Proceedings of the ACM Conference on Computer Supported Cooperative Work
TI - Game-theoretic models identify useful principles for peer collaboration in online learning platforms
VL - 26
ER -
TY - JOUR
AB - Direct reciprocity is a major mechanism for the evolution of cooperation. Several classical studies have suggested that humans should quickly learn to adopt reciprocal strategies to establish mutual cooperation in repeated interactions. On the other hand, the recently discovered theory of ZD strategies has found that subjects who use extortionate strategies are able to exploit and subdue cooperators. Although such extortioners have been predicted to succeed in any population of adaptive opponents, theoretical follow-up studies questioned whether extortion can evolve in reality. However, most of these studies presumed that individuals have similar strategic possibilities and comparable outside options, whereas asymmetries are ubiquitous in real world applications. Here we show with a model and an economic experiment that extortionate strategies readily emerge once subjects differ in their strategic power. Our experiment combines a repeated social dilemma with asymmetric partner choice. In our main treatment there is one randomly chosen group member who is unilaterally allowed to exchange one of the other group members after every ten rounds of the social dilemma. We find that this asymmetric replacement opportunity generally promotes cooperation, but often the resulting payoff distribution reflects the underlying power structure. Almost half of the subjects in a better strategic position turn into extortioners, who quickly proceed to exploit their peers. By adapting their cooperation probabilities consistent with ZD theory, extortioners force their co-players to cooperate without being similarly cooperative themselves. Comparison to non-extortionate players under the same conditions indicates a substantial net gain to extortion. Our results thus highlight how power asymmetries can endanger mutually beneficial interactions, and transform them into exploitative relationships. In particular, our results indicate that the extortionate strategies predicted from ZD theory could play a more prominent role in our daily interactions than previously thought.
AU - Hilbe, Christian
AU - Hagel, Kristin
AU - Milinski, Manfred
ID - 1322
IS - 10
JF - PLoS One
TI - Asymmetric power boosts extortion in an economic experiment
VL - 11
ER -