Results 1  10
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49
A Partial Approach to Model Checking
 INFORMATION AND COMPUTATION
, 1994
"... This paper presents a modelchecking method for lineartime temporal logic that can avoid most of the state explosion due to the modelling of concurrency by interleaving. The method relies on the concept of Mazurkiewicz's trace as a semantic basis and uses automatatheoretic techniques, including aut ..."
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Cited by 113 (5 self)
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This paper presents a modelchecking method for lineartime temporal logic that can avoid most of the state explosion due to the modelling of concurrency by interleaving. The method relies on the concept of Mazurkiewicz's trace as a semantic basis and uses automatatheoretic techniques, including automata that operate on words of ordinality higher than \omega.
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
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Cited by 72 (27 self)
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Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1
Quantitative Stochastic Parity Games
"... We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity w ..."
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Cited by 55 (24 self)
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We study perfectinformation stochastic parity games. These are twoplayer nonterminating games which are played on a graph with turnbased probabilistic transitions. A play results in an infinite path and the conflicting goals of the two players are!regular path properties, formalized as parity winning conditions. The qualitative solution of such a game amounts to computing the set of vertices from which a player has a strategy to win with probability 1 (or with positive probability). The quantitative solution amounts to computing the value of the game in every vertex, i.e., the highest probability with which a player can guarantee satisfaction of his own objective in a play that starts from the vertex. For the important special case of oneplayer stochastic parity games (parity Markov decision processes) we give polynomialtime algorithms both for the qualitative and the quantitative solution. The running time of the qualitative solution is O(d \Delta m 3=2) for graphs with m edges and d priorities. The quantitative solution is based on a linearprogramming formulation.
Implementation of Symbolic Model Checking for Probabilistic Systems
, 2002
"... In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilist ..."
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Cited by 50 (18 self)
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In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilistic model and a speci cation, such as \the message will be delivered with probability 1", \the probability of shutdown occurring is at most 0.02" or \the probability of a leader being elected within 5 rounds is at least 0.98", and can automatically verify if the speci cation is true in the model.
Quantitative Solution of OmegaRegular Games
"... We consider twoplayer games played for an infinite number of rounds, with ωregular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor s ..."
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Cited by 44 (16 self)
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We consider twoplayer games played for an infinite number of rounds, with ωregular winning conditions. The games may be concurrent, in that the players choose their moves simultaneously and independently, and probabilistic, in that the moves determine a probability distribution for the successor state. We introduce quantitative game µcalculus, and we show that the maximal probability of winning such games can be expressed as the fixpoint formulas in this calculus. We develop the arguments both for deterministic and for probabilistic concurrent games; as a special case, we solve probabilistic turnbased games with ωregular winning conditions, which was also open. We also characterize the optimality, and the memory requirements, of the winning strategies. In particular, we show that while memoryless strategies suffice for winning games with safety and reachability conditions, Büchi conditions require the use of strategies with infinite memory. The existence of optimal strategies, as opposed to εoptimal, is only guaranteed in games with safety winning conditions.
Weak bisimulation for probabilistic systems
 CONCURRENCY THEORY, LNCS
, 2000
"... In this paper, we introduce weak bisimulation in the framework of Labeled Concurrent Markov Chains, that is, probabilistic transition systems which exhibit both probabilistic and nondeterministic behavior. By resolving the nondeterminism present, these models can be decomposed into a possibly infini ..."
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Cited by 40 (3 self)
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In this paper, we introduce weak bisimulation in the framework of Labeled Concurrent Markov Chains, that is, probabilistic transition systems which exhibit both probabilistic and nondeterministic behavior. By resolving the nondeterminism present, these models can be decomposed into a possibly infinite number of computation trees. We show that in order to compute weak bisimulation it is sufficient to restrict attention to only a finite number of these computations. Finally, we present an algorithm for deciding weak bisimulation which has polynomialtime complexity in the number of states of the transition system.
How to Specify and Verify the LongRun Average Behavior of Probabilistic Systems
 In Proc. LICS'98
, 1998
"... Longrun average properties of probabilistic systems refer to the average behavior of the system, measured over a period of time whose length diverges to infinity. These properties include many relevant performance and reliability indices, such as system throughput, average response time, and mean t ..."
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Cited by 38 (3 self)
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Longrun average properties of probabilistic systems refer to the average behavior of the system, measured over a period of time whose length diverges to infinity. These properties include many relevant performance and reliability indices, such as system throughput, average response time, and mean time between failures. In this paper, we argue that current formal specification methods cannot be used to specify longrun average properties of probabilistic systems. To enable the specification of these properties, we propose an approach based on the concept of experiments. Experiments are labeled graphs that can be used to describe behavior patterns of interest, such as the request for a resource followed by either a grant or a rejection. Experiments are meant to be performed infinitely often, and it is possible to specify their longrun average outcome or duration. We propose simple extensions of temporal logics based on experiments, and we present modelchecking algorithms for the verif...
Recursive Markov decision processes and recursive stochastic games
 In Proc. of 32nd Int. Coll. on Automata, Languages, and Programming (ICALP’05
, 2005
"... Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural ..."
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Cited by 37 (9 self)
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Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural model for verification of probabilistic procedural programs and related systems involving both recursion and probabilistic behavior. RMCs define a class of denumerable Markov chains with a rich theory generalizing that of stochastic contextfree grammars and multitype branching processes, and they are also intimately related to probabilistic pushdown systems. RMDPs & RSSGs extend RMCs with one controller or two adversarial players, respectively. Such extensions are useful for modeling nondeterministic and concurrent behavior, as well as modeling a system’s interactions with an environment. We provide a number of upper and lower bounds for deciding, given an RMDP (or RSSG) A and probability p, whether player 1 has a strategy to force termination at a desired exit with probability at least p. We also address “qualitative ” termination questions, where p = 1, and model checking questions. 1
Distinguishing Tests for Nondeterministic and Probabilistic Machines
, 1995
"... We study the problem of uniquely identifying the initial state of a given finitestate machine from among a set of possible choices, based on the inputoutput behavior. Equivalently, given a set of machines, the problem is to design a test that distinguishes among them. We consider nondeterministic ..."
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Cited by 36 (4 self)
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We study the problem of uniquely identifying the initial state of a given finitestate machine from among a set of possible choices, based on the inputoutput behavior. Equivalently, given a set of machines, the problem is to design a test that distinguishes among them. We consider nondeterministic machines as well as probabilistic machines. In both cases, we show that it is Pspacecomplete to decide whether there is a preset distinguishing strategy (i.e. a sequence of inputs fixed in advance), and it is Exptimecomplete to decide whether there is an adaptive distinguishing strategy (i.e. when the next input can be chosen based on the outputs observed so far). The probabilistic testing is closely related to probabilistic games, or Markov Decision Processes, with incomplete information. We also provide optimal bounds for deciding whether such games have strategies winning with probability 1. 1 Introduction Finitestate machines have been widely used to model systems in diverse areas o...
Concurrent OmegaRegular Games
, 2000
"... We consider twoplayer games which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider ..."
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Cited by 33 (10 self)
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We consider twoplayer games which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider omegaregular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves. This gives rise to the following qualitative modes of winning, which can be studied without numerical considerations concerning probabilities: surewin (player 1 can ensure winning with certainty), almostsurewin (player 1 can ensure winning with probability 1), limitwin (player 1 can ensure winning with probability arbitrarily close to 1), boundedwin (player 1 can ensure winning with probability bounded away from 0), positivewin (player 1 can ensure winning with positive probability), and existwin (player 1 can ensure that at least one possible outcome of the game satisfies the winning condition). We provide algorithms for computing the sets of winning states for each of these winning modes. In particular, we solve concurrent Rabinchain games in ÒÇ Ñ time, where Ò is the size of the game structure and Ñ is the number of pairs in the Rabinchain condition. While this complexity is in line with traditional turnbased games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turnbased games. This is because concurrent games violate two of the most fundamental properties of turnbased games. First, concurrent games are not determined, but rather exhibit a more general duality property which involves multiple modes of winning. Second, winning strategies for concurrent games may require infinite memory.