Results 1  10
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14
Model Checking Probabilistic Pushdown Automata
, 2004
"... We consider the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various probabilistic logics. We start with properties that can be formulated as instances of a generalized random walk problem. We prove that both qualitative and quantitative model check ..."
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Cited by 63 (27 self)
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We consider the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various probabilistic logics. We start with properties that can be formulated as instances of a generalized random walk problem. We prove that both qualitative and quantitative model checking for this class of properties and pPDA is decidable. Then we show that model checking for the qualitative fragment of the logic PCTL and pPDA is also decidable. Moreover, we develop an errortolerant model checking algorithm for general PCTL and the subclass of stateless pPDA. Finally, we consider the class of properties definable by deterministic B uchi automata, and show that both qualitative and quantitative model checking for pPDA is decidable. 1.
On the decidability of temporal properties of probabilistic pushdown automata
 In Proc. of STACS’05
, 2005
"... Abstract. We consider qualitative and quantitative modelchecking problems for probabilistic pushdown automata (pPDA) and various temporal logics. We prove that the qualitative and quantitative modelchecking problem for ωregular properties and pPDA is in 2EXPSPACE and 3EXPTIME, respectively. We ..."
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Cited by 30 (9 self)
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Abstract. We consider qualitative and quantitative modelchecking problems for probabilistic pushdown automata (pPDA) and various temporal logics. We prove that the qualitative and quantitative modelchecking problem for ωregular properties and pPDA is in 2EXPSPACE and 3EXPTIME, respectively. We also prove that modelchecking the qualitative fragment of the logic PECTL ∗ for pPDA is in 2EXPSPACE, and modelchecking the qualitative fragment of PCTL for pPDA is in EXPSPACE. Furthermore, modelchecking the qualitative fragment of PCTL is shown to be EXPTIMEhard even for stateless pPDA. Finally, we show that PCTL modelchecking is undecidable for pPDA, and PCTL + modelchecking is undecidable even for stateless pPDA. 1
Verification of probabilistic systems with faulty communication
 IN PROCEEDINGS OF FOSSACS 2003
, 2003
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Reasoning About Probabilistic Lossy Channel Systems
"... We consider the problem of deciding whether an infinitestate system (expressed as a Markov chain) satisfies a correctness property with probability 1. This problem is, of course, undecidable for general infinitestate systems. We focus our attention on the model of probabilistic lossy channel syste ..."
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Cited by 18 (6 self)
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We consider the problem of deciding whether an infinitestate system (expressed as a Markov chain) satisfies a correctness property with probability 1. This problem is, of course, undecidable for general infinitestate systems. We focus our attention on the model of probabilistic lossy channel systems consisting of finitestate processes that communicating over unbounded lossy FIFO channels. Abdulla and Jonsson have shown that safety properties are decidable while progress properties are not for nonprobabilistic lossy channel systems. Under assumptions of "sufficiently high" probability of loss, Baier and Engelen have shown how to check whether a property holds of probabilistic lossy channel system with probability 1. In this paper we show that the problem of checking whether a progress property holds with probability 1 is undecidable, if the assumption about "sufficiently high" probability of loss is omitted. More surprisingly, we show that checking whether safety prop...
The verification of probabilistic lossy channel systems
 In Validation of Stochastic Systems – A Guide to Current Research, LNCS 2925
, 2004
"... Abstract. Lossy channel systems (LCS’s) are systems of finite state automata that communicate via unreliable unbounded fifo channels. Several probabilistic versions of these systems have been proposed in recent years, with the two aims of modeling more faithfully the losses of messages, and circumve ..."
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Cited by 13 (0 self)
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Abstract. Lossy channel systems (LCS’s) are systems of finite state automata that communicate via unreliable unbounded fifo channels. Several probabilistic versions of these systems have been proposed in recent years, with the two aims of modeling more faithfully the losses of messages, and circumventing undecidabilities by some kind of randomization. We survey these proposals and the verification techniques they support. 1
Probabilistic Models for Reo Connector Circuits
 Reasoning About ChannelBased Component Connectors 15
, 2005
"... Constraint automata have been used as an operational model for Reo which o#ers a channelbased framework to compose complex component connectors. In this paper, we introduce a variant of constraint automata with discrete probabilities and nondeterminism, called probabilistic constraint automata. The ..."
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Cited by 4 (1 self)
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Constraint automata have been used as an operational model for Reo which o#ers a channelbased framework to compose complex component connectors. In this paper, we introduce a variant of constraint automata with discrete probabilities and nondeterminism, called probabilistic constraint automata. These can serve for compositional reasoning about connector components, modelled by Reo circuits with unreliable channels, e.g., that might loose or corrupt messages, or channels with random output values that, e.g., can be helpful to model randomized coordination principles.
Verification of Probabilistic Recursive Sequential Programs
, 2007
"... This work studies algorithmic verification of infinitestate probabilistic systems generated by probabilistic pushdown automata (pPDA). Probabilistic pushdown automata are obtained as a probabilistic variant of pushdown automata that proved to be a successful abstract model of recursive sequential p ..."
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Cited by 3 (1 self)
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This work studies algorithmic verification of infinitestate probabilistic systems generated by probabilistic pushdown automata (pPDA). Probabilistic pushdown automata are obtained as a probabilistic variant of pushdown automata that proved to be a successful abstract model of recursive sequential programs. The main aim of this work is to study decidability and complexity of the problem whether a given probabilistic system generated by a pPDA satisfies a given property expressed in a suitable formalism. There are plenty of formalisms available for specifying properties of probabilistic systems. In this work we consider various temporal properties expressed by finitestate automata on infinite words and formulae of temporal logics, longrun average properties, and properties connected with expected behavior. Concerning temporal logics, we consider both linear and branching time ones. Among others we consider linear temporal logic (LTL) and probabilistic computation tree logic (PCTL), which is a probabilistic variant of the wellknown logic CTL. We also consider a general logic PECTL ∗ , which combines automata based
Eager Markov chains
 In Proc. ATVA ’06, 4Ø�Int. Symp. on Automated Technology for Verification and Analysis
, 2006
"... Abstract. We consider infinitestate discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more thanÒsteps is bounded by some exponentially decreasing function�(Ò). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel ..."
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Cited by 3 (2 self)
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Abstract. We consider infinitestate discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more thanÒsteps is bounded by some exponentially decreasing function�(Ò). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel Systems, Probabilistic Vector Addition Systems with States, and Noisy Turing Machines, and that the bounding function�(Ò) can be effectively constructed for them. Furthermore, we study the problem of computing the expected reward (or cost) of runs until reaching the final states, where rewards are assigned to individual runs by computable reward functions. For eager Markov chains, an effective path exploration scheme, based on forward reachability analysis, can be used to approximate the expected reward upto an arbitrarily small error. 1
A Note on the AttractorProperty of InfiniteState Markov Chains
, 2005
"... In the past 5 years, a series of verification algorithms has been proposed for infinite Markov chains that have a finite attractor, i.e., a set that will be visited infinitely often almost surely starting from any state. In this paper, we establish a sufficient criterion for the existence of an attr ..."
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Cited by 3 (2 self)
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In the past 5 years, a series of verification algorithms has been proposed for infinite Markov chains that have a finite attractor, i.e., a set that will be visited infinitely often almost surely starting from any state. In this paper, we establish a sufficient criterion for the existence of an attractor. We show that if the states of a Markov chain can be given levels (positive integers) such that the expected next level for states at some level n > 0 if less than n for some positive D, then the states at level 0 constitute an attractor for the chain. As an application, we obtain a direct proof that some probabilistic channel systems combining message losses with duplication and insertion errors have a finite attractor.
Limiting Behavior of Markov Chains with Eager Attractors
, 2006
"... We consider discrete infinitestate Markov chains which contain an eager finite attractor. A finite attractor is a finite subset of states that is eventually reached with probability 1 from every other state, and the eagerness condition requires that the probability of avoiding the attractor in n o ..."
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Cited by 2 (2 self)
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We consider discrete infinitestate Markov chains which contain an eager finite attractor. A finite attractor is a finite subset of states that is eventually reached with probability 1 from every other state, and the eagerness condition requires that the probability of avoiding the attractor in n or more steps after leaving it is exponentially bounded in n. Examples of such Markov chains are those induced by probabilistic lossy channel