Branching-Time Model-Checking of Probabilistic Pushdown Automata

Brázdil, Tomǎš; Brožek, Václav; Forejt, Vojtěch

doi:10.1016/j.entcs.2009.05.031

Cited by 5 publications

(19 citation statements)

References 20 publications

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“…Our model of PHORS is expressive enough to accurately model probabilistic higher-order functions, but the underlying non-probabilistic language (i.e., HORS, obtained by removing probabilistic choice) is not Turing-complete; thus, we can hope for existence of algorithmic solutions to some of the verification problems (in fact, we can decide whether the termination probability of PHORS is 0, by reduction to a model checking problem for non-probabilistic HORS). Through the well-known correspondence between HORS and (collapsible) higher-order pushdown automata [41,32], PHORS can be considered a higher-order extension of probabilistic pushdown systems [7,6] and of recursive Markov chains [66], the computation models used in previous work on model checking of probabilistic recursive programs. We can also view PHORS as an extension of the λY -calculus [62] with probabilities, just like HORS can be viewed as an alternative presentation of the λY -calculus.…”

Section: Introductionmentioning

confidence: 99%

“…As we will see in Section 2, the two questions above on the listgen program can also be reduced to problems of computing the termination probability of PHORS. Note also that computing the termination (or equivalently, reachability) probability has been a key to solving more general model checking problems (such as LTL/CTL model checking) for recursive programs [66,6].…”

Section: Introductionmentioning

confidence: 99%

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On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Kobayashi

Lago

Grellois

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem -or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (but possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORSs, and confirmed that the procedure works well through preliminary experiments that are reported at the end of the article.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Kobayashi

Lago

Grellois

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…Roughly, Markov chains are probabilistic transition systems which are accepted [3] as the most popular operational model for the evaluation of performance and dependability of information-processing systems. For convenience, the following definition is re-stated from [18]. Definition 2.3.…”

Section: Markov Decision Processmentioning

confidence: 99%

“…In the literature on probabilistic formal verification, the formal model for probabilistic discrete systems was often depicted by Markov chains [18,3,8,4,11], which are useful in a number of areas including engineering. Recently, many researchers [3,4,11] suggested to take advantage of the more general case of Markov chains, i.e.…”

Section: Introductionmentioning

confidence: 99%

Model-checking branching-time properties of probabilistic automata and probabilistic one-counter automata

Lin¹

2015

Preprint

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This paper studies the problem of model-checking of probabilistic automaton and probabilistic one-counter automata against probabilistic branching-time temporal logics (PCTL and PCTL * ). We show that it is undecidable for these problems.We first show, by reducing to emptiness problem of probabilistic automata, that the modelchecking of probabilistic finite automata against branching-time temporal logics are undecidable. And then, for each probabilistic automata, by constructing a probabilistic one-counter automaton with the same behavior as questioned probabilistic automata the undecidability of model-checking problems against branching-time temporal logics are derived, herein.

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“…To the author's knowledge, the verification of probabilistic programs was considered first in the 1980s, for example [12] by Vardi. During recent two decades, researchers have paid their attention to model-checking of probabilistic infinite-state systems, for instance [8,7] by Esparza. One of such probabilistic infinite-state systems is probabilistic pushdown process, which was called "probabilistic pushdown automata" in [8,7,16,15]. Here, we reserve "probabilistic pushdown automata" for the probabilistic extension of nondeterministic pushdown automata [14,6].…”

Section: Introductionmentioning

confidence: 99%