Results 1  10
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24
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 79 (24 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
"... 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 pro ..."
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Cited by 42 (11 self)
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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.
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 20 (7 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 19 (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
Analysis and Prediction of the LongRun Behavior of Probabilistic Sequential Programs with Recursion (Extended Abstract)
"... We introduce a family of longrun average properties of Markov chains that are useful for purposes of performance and reliability analysis, and show that these properties can effectively be checked for a subclass of infinitestate Markov chains generated by probabilistic programs with recursive proc ..."
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Cited by 18 (9 self)
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We introduce a family of longrun average properties of Markov chains that are useful for purposes of performance and reliability analysis, and show that these properties can effectively be checked for a subclass of infinitestate Markov chains generated by probabilistic programs with recursive procedures. We also show how to predict these properties by analyzing finite prefixes of runs, and present an efficient prediction algorithm for the mentioned subclass of Markov chains.
Verifying infinite Markov chains with a finite attractor or the global coarseness property
 In Proc. LICS ’0521th IEEE Int. Symp. on Logic in Computer Science
, 2005
"... We consider infinite Markov chains which either have a finite attractor or satisfy the global coarseness property. Markov chains derived from probabilistic lossy channel systems (PLCS) or probabilistic vector addition systems with states (PVASS) are classic examples for these types, respectively. ..."
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Cited by 12 (3 self)
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We consider infinite Markov chains which either have a finite attractor or satisfy the global coarseness property. Markov chains derived from probabilistic lossy channel systems (PLCS) or probabilistic vector addition systems with states (PVASS) are classic examples for these types, respectively. We consider three different variants of the reachability problem and the repeated reachability problem: The qualitative problem, i.e., deciding if the probability is one (or zero); the approximate quantitative problem, i.e., computing the probability upto arbitrary precision; the exact quantitative problem, i.e., computing probabilities exactly. We express the qualitative problem in abstract terms for Markov chains with a finite attractor and for globally coarse Markov chains, and show an almost complete picture of its decidability of PLCS and PVASS. We also show that the path enumeration algorithm of [19] terminates for our types of Markov chain and can thus be used to solve the approximate quantitative reachability problem. Furthermore, a modified variant of this algorithm can solve the approximate quantitative repeated reachability problem for Markov chains with a finite attractor. Finally, we show that the exact probability of (repeated) reachability cannot be effectively expressed in the firstorder theory of the reals (IR; +; ;) for either PLCS or PVASS (unlike for other probabilistic models, e.g., probabilistic pushdown automata [14, 15, 13]). 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 10 (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 8 (2 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
Computable Fixpoints in WellStructured Symbolic Model Checking
 FMSD
"... We prove a general finitetime convergence theorem for fixpoint expressions over a wellquasiordered set. This has immediate applications for the verification of wellstructured systems, where a main issue is the computability of fixpoint expressions, and in particular for gametheoretical propert ..."
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Cited by 8 (0 self)
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We prove a general finitetime convergence theorem for fixpoint expressions over a wellquasiordered set. This has immediate applications for the verification of wellstructured systems, where a main issue is the computability of fixpoint expressions, and in particular for gametheoretical properties and probabilistic systems where nesting and alternation of least and greatest fixpoints are common.