On the Decidability of Temporal Properties of Probabilistic Pushdown Automata

Brázdil, Tomǎš; Kučera, Antonín; Stražovský, Oldřich

doi:10.1007/978-3-540-31856-9_12

Cited by 62 publications

(79 citation statements)

References 30 publications

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“…Since the model-checking problem for qualitative PCTL and fully probabilistic BPA (i.e., the subclass of 1 1 2 -player BPA games where Γ 2 = ∅) is known to be EXPTIME-hard [3], we obtain the following:…”

Section: Let Us Consider An Ero (S T ) Where C(s) = {X Y Z H} Andmentioning

confidence: 99%

“…More precisely, our algorithm is polynomial in the size of a given BPA and exponential in the size of a given formula (hence, the algorithm becomes polynomial for each fixed formula). Since there is a matching EXPTIME lower bound [3], we yield the EXPTIME-completeness of the problem. As a consequence we also obtain the EXPTIME-completeness of the model-checking problem for fully probabilistic BPA and qualitative PCTL (fully probabilistic BPA correspond to a subclass of 1 1 2 -player BPA games where all heads are probabilistic).…”

mentioning

confidence: 99%

“…As a consequence we also obtain the EXPTIME-completeness of the model-checking problem for fully probabilistic BPA and qualitative PCTL (fully probabilistic BPA correspond to a subclass of 1 1 2 -player BPA games where all heads are probabilistic). This problem has been studied in [4,3], but the best known upper complexity bound was EXPSPACE.…”

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confidence: 99%

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Reachability in Recursive Markov Decision Processes

Brázdil

Brožek

Forejt

et al. 2006

CONCUR 2006 – Concurrency Theory

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Abstract. We consider a class of infinite-state Markov decision processes generated by stateless pushdown automata. This class corresponds to 1 1 2 -player games over graphs generated by BPA systems or (equivalently) 1-exit recursive state machines. An extended reachability objective is specified by two sets S and T of safe and terminal stack configurations, where the membership to S and T depends just on the top-of-the-stack symbol. The question is whether there is a suitable strategy such that the probability of hitting a terminal configuration by a path leading only through safe configurations is equal to (or different from) a given x ∈ {0, 1}. We show that the qualitative extended reachability problem is decidable in polynomial time, and that the set of all configurations for which there is a winning strategy is effectively regular. More precisely, this set can be represented by a deterministic finite-state automaton with a fixed number of control states. This result is a generalization of a recent theorem by Etessami & Yannakakis which says that the qualitative termination for 1-exit RMDPs (which exactly correspond to our 1 1 2 -player BPA games) is decidable in polynomial time. Interestingly, the properties of winning strategies for the extended reachability objectives are quite different from the ones for termination, and new observations are needed to obtain the result. As an application, we derive the EXPTIME-completeness of the model-checking problem for 1 1 2 -player BPA games and qualitative PCTL formulae.

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Section: Let Us Consider An Ero (S T ) Where C(s) = {X Y Z H} Andmentioning

confidence: 99%

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confidence: 99%

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Reachability in Recursive Markov Decision Processes

Brázdil

Brožek

Forejt

et al. 2006

CONCUR 2006 – Concurrency Theory

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“…RMCs define a class of denumerable Markov chains with a rich theory generalizing that of Stochastic Context-Free Grammars (SCFGs) (see, e.g., [MS99]) and Multi-Type Branching Processes ( [Har63]), both of which correspond to 1-exit RMCs: RMCs in which each component Markov chain has 1 terminating exit state where it can return control back to a component that called it. RMCs are also intimately related to probabilistic Pushdown Systems (pPDSs), which have also been studied recently in connection to verification of probabilistic programs ( [EKM04,BKS05]). …”

Section: Introductionmentioning

confidence: 99%

“…As mentioned, 1-exit RMCs correspond to both MT-BPs and SCFGs (see, e.g., [Har63] and [MS99]), while general RMCs are intimately related to probabilistic Pushdown Systems (pPDSs). Model checking questions for pPDSs, for both linear and branching time properties, have also been recently studied in [EKM04,BKS05]. [EE04] is an early survey paper which summarizes the results in only the papers [EKM04,EY05a,BKS05].…”

Section: Introductionmentioning

confidence: 99%

Recursive Markov Decision Processes and Recursive Stochastic Games

Etessami

Yannakakis

2005

Automata, Languages and Programming

112

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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 context-free grammars and multi-type 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.

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Computing the Expected Accumulated Reward and Gain for a Subclass of Infinite Markov Chains

Brázdil

Kučera

2005

Lecture Notes in Computer Science

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On the Decidability of Temporal Properties of Probabilistic Pushdown Automata

Cited by 62 publications

References 30 publications

Reachability in Recursive Markov Decision Processes

Reachability in Recursive Markov Decision Processes

Recursive Markov Decision Processes and Recursive Stochastic Games

Computing the Expected Accumulated Reward and Gain for a Subclass of Infinite Markov Chains

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