The complexity of probabilistic verification

Courcoubetis, Costas; Yannakakis, Mihalis

doi:10.1145/210332.210339

Cited by 481 publications

(511 citation statements)

References 12 publications

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“…The technique used to prove this result significantly extends the technique developed for the proofs of decidability of the model checking problem for probabilistic temporal logics [4]. The expressive power of our logic is incomparable to the expressive power of probabilistic temporal logics.…”

Section: Introductionmentioning

confidence: 91%

“…Thus, from [3], there exists a computable finite complete deterministic automaton A on the alphabet AE accepting a language of finite words LðAÞ such that S, n 'ðtÞ iff the prefix of S of size n þ 1 belongs to LðAÞ. Therefore, given the automaton A and the finite probabilistic process M, we build a new finite probabilistic process M 0 , the 'product' of M and A following the same lines as in Section 4 of [4].…”

Section: Theoremmentioning

confidence: 99%

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A Logic of Probability with Decidable Model-Checking

Beauquier¹,

Rabinovich

Slissenko³

2002

Computer Science Logic

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A predicate logic of probability, close to the logics of probability of Halpern et al., is introduced. Our main result concerns the following model-checking problem: deciding whether a given formula holds on the structure defined by a given finite probabilistic process. We show that this model-checking problem is decidable for a rather large subclass of formulas of a second-order monadic logic of probability. We discuss also the decidability of satisfiability and compare our logic of probability with the probabilistic temporal logic pCTL*.

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Section: Introductionmentioning

confidence: 91%

Section: Theoremmentioning

confidence: 99%

A Logic of Probability with Decidable Model-Checking

Beauquier¹,

Rabinovich

Slissenko³

2002

Computer Science Logic

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“…These problems may be closely interrelated: In classical semantics, both problems can be solved through the existence of alternating automata that are only exponential in the length of a CTL* formula ϕ, which accept the models of ϕ. It does not seem unlikely that similar solutions exist for almost-sure/observable semantics, taking into account that model-checking remains PSPACE-complete (Yannakakis PSPACE result for LTL model-checking [4] trivially extends to CTL*).…”

Section: Discussionmentioning

confidence: 99%

Synthesis for Probabilistic Environments

Schewe

2006

Automated Technology for Verification and Analysis

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Abstract. In synthesis we construct finite state systems from temporal specifications. While this problem is well understood in the classical setting of non-probabilistic synthesis, this paper suggests the novel approach of open synthesis under the assumptions of an environment that chooses its actions randomized rather than nondeterministically. Assuming a randomized environment inspires alternative semantics both for linear-time and branching-time logics. For linear-time, natural acceptance criteria are almost-sure and observable acceptance, where it suffices if the probability measure of accepting paths is 1 and greater than 0, respectively. We distinguish 0-environments, which can freely assign probabilities to each environment action, from ε-environments, where the probabilities assigned by the environment are bound from below by some ε > 0. While the results in case of 0-environments are essentially the same as for nondeterministic environments, the languages occurring in case of ε-environments are topologically different from the results for nondeterministic and 0-environments (in case of LTL, recognizable by weak alternating automata vs. recognizable by deterministic automata). The complexity of open synthesis is, in both cases, EXPTIME and 2EXPTIME-complete for CTL and LTL specifications, respectively.

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“…For P ⊆ Q, P ε is the set {(p, ε) | p ∈ P} so that ♦Q ε means that eventually a configuration with empty channels is reached. It is well-known that for any scheduler U, the set of paths starting in some configuration s and satisfying an LTL formula, or an ω-regular property, ϕ is measurable [32,16]. We write Pr U s |= ϕ for this measure.…”

Section: Ltl/ctl-notationmentioning

confidence: 99%

Symbolic Verification of Communicating Systems with Probabilistic Message Losses: Liveness and Fairness

Baier

Bertrand

Schnoebelen

2006

Lecture Notes in Computer Science

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Abstract. NPLCS's are a new model for nondeterministic channel systems where unreliable communication is modeled by probabilistic message losses. We show that, for ω-regular linear-time properties and finite-memory schedulers, qualitative model-checking is decidable. The techniques extend smoothly to questions where fairness restrictions are imposed on the schedulers. The symbolic procedure underlying our decidability proofs has been implemented and used to study a simple protocol handling two-way transfers in an unreliable setting.

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The complexity of probabilistic verification

Cited by 481 publications

References 12 publications

A Logic of Probability with Decidable Model-Checking

A Logic of Probability with Decidable Model-Checking

Synthesis for Probabilistic Environments

Symbolic Verification of Communicating Systems with Probabilistic Message Losses: Liveness and Fairness

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