TY - JOUR
AB - Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable.
AU - Boker, Udi
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 2038
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
TI - Temporal specifications with accumulative values
VL - 15
ER -
TY - JOUR
AB - A fundamental question in biology is the following: what is the time scale that is needed for evolutionary innovations? There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a population exploring a fitness landscape to find target sequences that encode new biological functions? Our key variable is the length, (Formula presented.) of the genetic sequence that undergoes adaptation. In computer science there is a crucial distinction between problems that require algorithms which take polynomial or exponential time. The latter are considered to be intractable. Here we develop a theoretical approach that allows us to estimate the time of evolution as function of (Formula presented.) We show that adaptation on many fitness landscapes takes time that is exponential in (Formula presented.) even if there are broad selection gradients and many targets uniformly distributed in sequence space. These negative results lead us to search for specific mechanisms that allow evolution to work on polynomial time scales. We study a regeneration process and show that it enables evolution to work in polynomial time.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Adlam, Ben
AU - Nowak, Martin
ID - 2039
IS - 9
JF - PLoS Computational Biology
TI - The time scale of evolutionary innovation
VL - 10
ER -
TY - CONF
AB - A standard technique for solving the parameterized model checking problem is to reduce it to the classic model checking problem of finitely many finite-state systems. This work considers some of the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable Monadic Second Order Logic formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases that model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.
AU - Aminof, Benjamin
AU - Kotek, Tomer
AU - Rubin, Sacha
AU - Spegni, Francesco
AU - Veith, Helmut
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2052
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Parameterized model checking of rendezvous systems
VL - 8704
ER -
TY - CONF
AB - In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a longstanding open problem concerning the representation of memoryless continuous time by memoryfull continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems.
AU - Hermanns, Holger
AU - Krčál, Jan
AU - Kretinsky, Jan
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2053
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Probabilistic bisimulation: Naturally on distributions
VL - 8704
ER -
TY - CONF
AB - We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.
AU - Chatterjee, Krishnendu
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2054
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Qualitative concurrent parity games: Bounded rationality
VL - 8704
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems.We focus on qualitative properties forMDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation ofMDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.We present an automated technique for assume-guarantee style reasoning for compositional analysis ofMDPs with qualitative properties by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Daca, Przemyslaw
ID - 2063
TI - CEGAR for qualitative analysis of probabilistic systems
VL - 8559
ER -
TY - JOUR
AB - The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2)-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
ID - 2141
IS - 3
JF - Journal of the ACM
TI - Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition
VL - 61
ER -
TY - CONF
AB - We study two-player (zero-sum) concurrent mean-payoff games played on a finite-state graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy); (2) the approximation problem lies in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP ∩ coNP is the long-standing best known bound). We present a variant of the strategy-iteration algorithm by Hoffman and Karp; show that both our algorithm and the classical value-iteration algorithm can approximate the value in exponential time; and identify a subclass where the value-iteration algorithm is a FPTAS. We also show that the exact value can be expressed in the existential theory of the reals, and establish square-root sum hardness for a related class of games.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 2162
IS - Part 2
TI - The complexity of ergodic mean payoff games
VL - 8573
ER -
TY - CONF
AB - We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable in general, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. From our results we derive new complexity results for partial-observation stochastic games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 2163
IS - Part 2
T2 - Lecture Notes in Computer Science
TI - Games with a weak adversary
VL - 8573
ER -
TY - JOUR
AB - Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Greimel, Karin
AU - Henzinger, Thomas A
AU - Hofferek, Georg
AU - Jobstmann, Barbara
AU - Könighofer, Bettina
AU - Könighofer, Robert
ID - 2187
IS - 3-4
JF - Acta Informatica
TI - Synthesizing robust systems
VL - 51
ER -
TY - CONF
AB - We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a master automaton and an array of slave automata, one for each G-subformula of φ. The slave automaton for G ψ is in charge of recognizing whether FG ψ holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows for various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.
AU - Esparza, Javier
AU - Kretinsky, Jan
ID - 2190
TI - From LTL to deterministic automata: A safraless compositional approach
VL - 8559
ER -
TY - JOUR
AB - In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 having perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algorithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 having perfect observation we show that nonelementarymemory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least nonelementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibit serious flaws in previous results of the literature: we show a nonelementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 2211
IS - 2
JF - ACM Transactions on Computational Logic (TOCL)
TI - Partial-observation stochastic games: How to win when belief fails
VL - 15
ER -
TY - CONF
AB - The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1/2-player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1/2-player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in time O(d·n2d·MeanGame) to compute the set of almost-sure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1/2-player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective).
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Oualhadj, Youssouf
ID - 2212
TI - Perfect-information stochastic mean-payoff parity games
VL - 8412
ER -
TY - CONF
AB - We consider two-player partial-observation stochastic games on finitestate graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are ε-regular conditions specified as parity objectives. The qualitative-analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). These qualitative-analysis problems are known to be undecidable. However in many applications the relevant question is the existence of finite-memory strategies, and the qualitative-analysis problems under finite-memory strategies was recently shown to be decidable in 2EXPTIME.We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Nain, Sumit
AU - Vardi, Moshe
ID - 2213
TI - The complexity of partial-observation stochastic parity games with finite-memory strategies
VL - 8412
ER -
TY - CONF
AB - The edit distance between two (untimed) traces is the minimum cost of a sequence of edit operations (insertion, deletion, or substitution) needed to transform one trace to the other. Edit distances have been extensively studied in the untimed setting, and form the basis for approximate matching of sequences in different domains such as coding theory, parsing, and speech recognition. In this paper, we lift the study of edit distances from untimed languages to the timed setting. We define an edit distance between timed words which incorporates both the edit distance between the untimed words and the absolute difference in time stamps. Our edit distance between two timed words is computable in polynomial time. Further, we show that the edit distance between a timed word and a timed language generated by a timed automaton, defined as the edit distance between the word and the closest word in the language, is PSPACE-complete. While computing the edit distance between two timed automata is undecidable, we show that the approximate version, where we decide if the edit distance between two timed automata is either less than a given parameter or more than δ away from the parameter, for δ > 0, can be solved in exponential space and is EXPSPACE-hard. Our definitions and techniques can be generalized to the setting of hybrid systems, and analogous decidability results hold for rectangular automata.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Majumdar, Ritankar
ID - 2216
TI - Edit distance for timed automata
ER -
TY - JOUR
AB - We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with κ limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for ε-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for ε-approximation, for all ε > 0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be ε-approximated in time polynomial in the size of the MDP and 1/ε, and exponential in the number of limit-average functions, for all ε > 0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results.
AU - Brázdil, Tomáš
AU - Brožek, Václav
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 2234
IS - 1
JF - Logical Methods in Computer Science
SN - 18605974
TI - Markov decision processes with multiple long-run average objectives
VL - 10
ER -
TY - JOUR
AB - Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP ∩ co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth.
AU - Grinshpun, Andrey
AU - Phalitnonkiat, Pakawat
AU - Rubin, Sasha
AU - Tarfulea, Andrei
ID - 2246
JF - Theoretical Computer Science
SN - 03043975
TI - Alternating traps in Muller and parity games
VL - 521
ER -
TY - CONF
AB - First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard.
AU - Aminof, Benjamin
AU - Rubin, Sasha
ID - 475
T2 - Electronic Proceedings in Theoretical Computer Science, EPTCS
TI - First cycle games
VL - 146
ER -
TY - JOUR
AB - Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Krinninger, Sebastian
AU - Nanongkai, Danupon
ID - 535
IS - 3
JF - Algorithmica
TI - Polynomial time algorithms for energy games with special weight structures
VL - 70
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5412
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5413
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation.
We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5414
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - Recently there has been a significant effort to add 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, several basic system properties such as average response time cannot be expressed with weighted automata. In this work, we introduce nested weighted automata as a new formalism for expressing important quantitative properties such as average response time. We establish an almost complete decidability picture for the basic decision problems for nested weighted automata, and illustrate its applicability in several domains.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5415
SN - 2664-1690
TI - Nested weighted automata
ER -
TY - GEN
AB - We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5418
SN - 2664-1690
TI - Games with a weak adversary
ER -
TY - GEN
AB - We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:
1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).
2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.
3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.
Our algorithms improve all existing results, and use very simple data structures.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5419
SN - 2664-1690
TI - Improved algorithms for reachability and shortest path on low tree-width graphs
ER -
TY - GEN
AB - We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 5420
SN - 2664-1690
TI - The value 1 problem for concurrent mean-payoff games
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are: (1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure). (2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5421
SN - 2664-1690
TI - The complexity of evolution on graphs
ER -
TY - GEN
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm- deadline real-time tasks based on multi-objective graphs: Given a taskset and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. a clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including D(over), that have been proposed in the past, for various tasksets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are tasksets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Kössler, Alexander
AU - Pavlogiannis, Andreas
AU - Schmid, Ulrich
ID - 5423
SN - 2664-1690
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5424
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 5426
SN - 2664-1690
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - GEN
AB - We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5427
SN - 2664-1690
TI - Optimal tree-decomposition balancing and reachability on low treewidth graphs
ER -
TY - GEN
AB - Simulation is an attractive alternative for language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. For non-deterministic automata, while language inclusion is PSPACE-complete, simulation can be computed in polynomial time. 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. Again, 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 for mean-payoff automata and the decidability is open for discounted-sum automata, whereas the (quantitative) simulation reduce to mean-payoff games and discounted-sum 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. For example, whereas for mean-payoff and discounted-sum games, the players do not need memory to play optimally; we show in contrast that for simulation games with Büchi acceptance conditions, (i) for mean-payoff objectives, optimal strategies for both players require infinite memory in general, and (ii) for discounted-sum objectives, optimal strategies need not exist for both players. While the simulation games with Büchi acceptance conditions are more complicated (e.g., due to infinite-memory requirements for mean-payoff objectives) as compared to their counterpart without Büchi acceptance conditions, we still present pseudo-polynomial time algorithms to solve simulation games with Büchi acceptance conditions for both weighted mean-payoff and weighted discounted-sum automata.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Velner, Yaron
ID - 5428
SN - 2664-1690
TI - Quantitative fair simulation games
ER -
TY - JOUR
AB - We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible to the problem of a logarithmic number of min-plus matrix multiplications of n×n-matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1+ε)-approximation algorithm for the problem and the running time of our algorithm is Õ(nωlog3(nW/ε)/ε),1 where O(nω) is the time required for the classic n×n-matrix multiplication and W is the maximum value of the weights. With an additional O(log(nW/ε)) factor in space a cycle with approximately optimal weight can be computed within the same time bound.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Krinninger, Sebastian
AU - Loitzenbauer, Veronika
AU - Raskin, Michael
ID - 1375
IS - C
JF - Theoretical Computer Science
TI - Approximating the minimum cycle mean
VL - 547
ER -
TY - CONF
AB - We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Randour, Mickael
AU - Raskin, Jean
ID - 2279
TI - Looking at mean-payoff and total-payoff through windows
VL - 8172
ER -
TY - GEN
AB - This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.
ED - Chatterjee, Krishnendu
ED - Sgall, Jiri
ID - 2292
SN - 978-3-642-40312-5
TI - Mathematical Foundations of Computer Science 2013
VL - 8087
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal EXPTIME-complete complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite-memory strategies. We also establish asymptotically optimal (exponential) memory bounds.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Tracol, Mathieu
ID - 2295
TI - What is decidable about partially observable Markov decision processes with omega-regular objectives
VL - 23
ER -
TY - JOUR
AB - The standard hardware design flow involves: (a) design of an integrated circuit using a hardware description language, (b) extensive functional and formal verification, and (c) logical synthesis. However, the above-mentioned processes consume significant effort and time. An alternative approach is to use a formal specification language as a high-level hardware description language and synthesize hardware from formal specifications. Our work is a case study of the synthesis of the widely and industrially used AMBA AHB protocol from formal specifications. Bloem et al. presented the first formal specifications for the AMBA AHB Arbiter and synthesized the AHB Arbiter circuit. However, in the first formal specification some important assumptions were missing. Our contributions are as follows: (a) We present detailed formal specifications for the AHB Arbiter incorporating the missing details, and obtain significant improvements in the synthesis results (both with respect to the number of gates in the synthesized circuit and with respect to the time taken to synthesize the circuit), and (b) we present formal specifications to generate compact circuits for the remaining two main components of AMBA AHB, namely, AHB Master and AHB Slave. Thus with systematic description we are able to automatically and completely synthesize an important and widely used industrial protocol.
AU - Godhal, Yashdeep
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
ID - 2299
IS - 5-6
JF - International Journal on Software Tools for Technology Transfer
TI - Synthesis of AMBA AHB from formal specification: A case study
VL - 15
ER -
TY - CONF
AB - We study the complexity of central controller synthesis problems for finite-state Markov decision processes, where the objective is to optimize both the expected mean-payoff performance of the system and its stability. e argue that the basic theoretical notion of expressing the stability in terms of the variance of the mean-payoff (called global variance in our paper) is not always sufficient, since it ignores possible instabilities on respective runs. For this reason we propose alernative definitions of stability, which we call local and hybrid variance, and which express how rewards on each run deviate from the run's own mean-payoff and from the expected mean-payoff, respectively. We show that a strategy ensuring both the expected mean-payoff and the variance below given bounds requires randomization and memory, under all the above semantics of variance. We then look at the problem of determining whether there is a such a strategy. For the global variance, we show that the problem is in PSPACE, and that the answer can be approximated in pseudo-polynomial time. For the hybrid variance, the analogous decision problem is in NP, and a polynomial-time approximating algorithm also exists. For local variance, we show that the decision problem is in NP. Since the overall performance can be traded for stability (and vice versa), we also present algorithms for approximating the associated Pareto curve in all the three cases. Finally, we study a special case of the decision problems, where we require a given expected mean-payoff together with zero variance. Here we show that the problems can be all solved in polynomial time.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 2305
T2 - 28th Annual ACM/IEEE Symposium
TI - Trading performance for stability in Markov decision processes
ER -
TY - CONF
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 both finite-state game graphs, and recursive game graphs (or pushdown game graphs) that model the control flow of sequential programs with recursion. The objectives we study are multidimensional mean-payoff objectives, where the goal of player 1 is to ensure that the mean-payoff is non-negative in all dimensions. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation. Our main contributions are as follows: (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 the weights are fixed; whereas if the number of dimensions is arbitrary, then the problem is known to be coNP-complete. (2) We show that pushdown graphs with multidimensional mean-payoff objectives can be solved in polynomial time. For both (1) and (2) our algorithms are based on hyperplane separation technique. (3) For pushdown games under global strategies both one and multidimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multidimensional problem is also undecidable; under modular strategies the one-dimensional problem is NP-complete. We show that if the number of modules, the number of exits, and the maximal absolute value of the weights are fixed, then pushdown games under modular strategies with one-dimensional mean-payoff objectives can be solved in polynomial time, and if either the number of exits or the number of modules is unbounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multidimensional mean-payoff games or pushdown games under modular strategies with one-dimensional mean-payoff objectives would imply the fixed parameter tractability of parity games.
AU - Chatterjee, Krishnendu
AU - Velner, Yaron
ID - 2329
TI - Hyperplane separation technique for multidimensional mean-payoff games
VL - 8052
ER -
TY - CONF
AB - We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth k, we present two improved static algorithms for both the problems that run in time O(n·k 2.38·2k ) and O(m·logn· k), respectively, where n is the number of states and m is the number of edges, significantly improving the previous known O(n·k·√n· k) bound for low treewidth. We also present decremental algorithms for both problems for MDPs with constant treewidth that run in amortized logarithmic time, which is a huge improvement over the previously known algorithms that require amortized linear time.
AU - Chatterjee, Krishnendu
AU - Ła̧Cki, Jakub
ID - 2444
TI - Faster algorithms for Markov decision processes with low treewidth
VL - 8044
ER -
TY - CONF
AB - The model-checking problem for probabilistic systems crucially relies on the translation of LTL to deterministic Rabin automata (DRW). Our recent Safraless translation [KE12, GKE12] for the LTL(F,G) fragment produces smaller automata as compared to the traditional approach. In this work, instead of DRW we consider deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW). The Safraless translation of LTL(F,G) formulas to DGRW results in smaller automata as compared to DRW. We present algorithms for probabilistic model-checking as well as game solving for DGRW conditions. Our new algorithms lead to improvement both in terms of theoretical bounds as well as practical evaluation. We compare PRISM with and without our new translation, and show that the new translation leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Gaiser, Andreas
AU - Kretinsky, Jan
ID - 2446
TI - Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis
VL - 8044
ER -
TY - JOUR
AB - We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned according to some coverage criterion and the objective of the tester is to maximize the set of partitions (or coverage goals) visited during the game. We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems. For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is coNP-complete. Our proof technique for reset games uses randomized testing strategies that circumvent the exponentially large memory requirement of deterministic testing strategies. We also discuss the memory requirement for deterministic strategies and extensions of our results to other models, such as pushdown systems and timed systems.
AU - Chatterjee, Krishnendu
AU - Alfaro, Luca
AU - Majumdar, Ritankar
ID - 2814
IS - 2
JF - International Journal of Foundations of Computer Science
TI - The complexity of coverage
VL - 24
ER -
TY - JOUR
AB - In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics.
AU - Božić, Ivana
AU - Reiter, Johannes
AU - Allen, Benjamin
AU - Antal, Tibor
AU - Chatterjee, Krishnendu
AU - Shah, Preya
AU - Moon, Yo
AU - Yaqubie, Amin
AU - Kelly, Nicole
AU - Le, Dung
AU - Lipson, Evan
AU - Chapman, Paul
AU - Diaz, Luis
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 2816
JF - eLife
TI - Evolutionary dynamics of cancer in response to targeted combination therapy
VL - 2
ER -
TY - JOUR
AB - The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.
AU - Novak, Sebastian
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 2817
JF - Journal of Theoretical Biology
TI - Density games
VL - 334
ER -
TY - CONF
AB - We introduce quantatitive timed refinement metrics and quantitative timed simulation functions, incorporating zenoness checks, for timed systems. These functions assign positive real numbers between zero and infinity which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximum timing mismatch that can arise, (2) the "steady-state" maximum timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation functions to within any desired degree of accuracy. In order to compute the values of the quantitative simulation functions, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives for player 1, and then use these algorithms to compute the values of the quantitative timed simulation functions.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 2819
T2 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control
TI - Quantitative timed simulation functions and refinement metrics for real-time systems
VL - 1
ER -
TY - CONF
AB - In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games.
AU - Chatterjee, Krishnendu
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 2820
SN - 978-1-4503-1567-8
T2 - Proceedings of the 16th International conference on Hybrid systems: Computation and control
TI - Automated analysis of real-time scheduling using graph games
ER -
TY - JOUR
AB - We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a Zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a logarithmic (in the number of clocks) number of memory bits (i.e. a linear number of memory states). Precisely, we show that for safety objectives, a memory of size (3 + lg (| C | + 1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential memory states bound. We also settle the open question of whether winning region-based strategies require memory for safety objectives by showing with an example the necessity of memory for such strategies to win for safety objectives. Finally, we show that the decision problem of determining if there exists a receptive player-1 winning strategy for safety objectives is EXPTIME-complete over timed automaton games.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 2824
JF - Information and Computation
TI - Synthesis of memory-efficient, clock-memory free, and non-Zeno safety controllers for timed systems
VL - 228-229
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(n · √ m) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs have constant out-degree, and then our symbolic algorithm takes O(n · √ n) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(n · √ K) symbolic steps, where K is the maximal number of edges of strongly connected components (scc's) of the MDP. The win-lose algorithm requires symbolic computation of scc's. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5×n symbolic steps, whereas our new algorithm takes 4×n symbolic steps.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 2831
IS - 3
JF - Formal Methods in System Design
TI - Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives
VL - 42
ER -
TY - JOUR
AB - We study the automatic synthesis of fair non-repudiation protocols, a class of fair exchange protocols, used for digital contract signing. First, we show how to specify the objectives of the participating agents and the trusted third party as path formulas in linear temporal logic and prove that the satisfaction of these objectives imply fairness; a property required of fair exchange protocols. We then show that weak (co-operative) co-synthesis and classical (strictly competitive) co-synthesis fail, whereas assume-guarantee synthesis (AGS) succeeds. We demonstrate the success of AGS as follows: (a) any solution of AGS is attack-free; no subset of participants can violate the objectives of the other participants; (b) the Asokan-Shoup-Waidner certified mail protocol that has known vulnerabilities is not a solution of AGS; (c) the Kremer-Markowitch non-repudiation protocol is a solution of AGS; and (d) AGS presents a new and symmetric fair non-repudiation protocol that is attack-free. To our knowledge this is the first application of synthesis to fair non-repudiation protocols, and our results show how synthesis can both automatically discover vulnerabilities in protocols and generate correct protocols. The solution to AGS can be computed efficiently as the secure equilibrium solution of three-player graph games.
AU - Chatterjee, Krishnendu
AU - Raman, Vishwanath
ID - 2836
IS - 4
JF - Formal Aspects of Computing
TI - Assume-guarantee synthesis for digital contract signing
VL - 26
ER -
TY - JOUR
AB - We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless ε-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an ε-optimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game. © 2012 Elsevier Inc.
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Henzinger, Thomas A
ID - 2854
IS - 5
JF - Journal of Computer and System Sciences
TI - Strategy improvement for concurrent reachability and turn based stochastic safety games
VL - 79
ER -