TY - CONF
AB - We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties inMDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or discounted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Forejt, Vojtěch
AU - Kretinsky, Jan
AU - Kwiatkowska, Marta
AU - Parker, David
AU - Ujma, Mateusz
ED - Cassez, Franck
ED - Raskin, Jean-François
ID - 2027
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Verification of markov decision processes using learning algorithms
VL - 8837
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 - 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 - JOUR
AB - Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.
AU - Chatterjee, Krishnendu
AU - Randour, Mickael
AU - Raskin, Jean
ID - 2716
IS - 3-4
JF - Acta Informatica
TI - Strategy synthesis for multi-dimensional quantitative objectives
VL - 51
ER -
TY - JOUR
AB - The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.
AU - Cerny, Pavol
AU - Chmelik, Martin
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 1733
IS - 3
JF - Theoretical Computer Science
TI - Interface simulation distances
VL - 560
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 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 - 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 -