Deciding Probabilistic Bisimilarity Over Infinite-State Probabilistic Systems

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

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Decay rates and cutoff for convergence and hitting times of Markov chains with countably infinite state space

10.1239/aap/999187903 ◽

2001 ◽

Vol 33 (1) ◽

pp. 188-205 ◽

Cited By ~ 10

Author(s):

Servet Martínez ◽

Bernard Ycart

Keyword(s):

Markov Chains ◽

State Space ◽

Decay Rates ◽

Hitting Times ◽

Countably Infinite ◽

Infinite State

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Local model checking for infinite state spaces

Theoretical Computer Science ◽

10.1016/0304-3975(92)90183-g ◽

1992 ◽

Vol 96 (1) ◽

pp. 157-174 ◽

Cited By ~ 40

Author(s):

Julian Bradfield ◽

Colin Stirling

Keyword(s):

Model Checking ◽

Local Model ◽

State Spaces ◽

Infinite State ◽

Local Model Checking

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Model Completeness, Uniform Interpolants and Superposition Calculus

Journal of Automated Reasoning ◽

10.1007/s10817-021-09596-x ◽

2021 ◽

Author(s):

Diego Calvanese ◽

Silvio Ghilardi ◽

Alessandro Gianola ◽

Marco Montali ◽

Andrey Rivkin

Keyword(s):

Automated Reasoning ◽

Quantifier Elimination ◽

Effective Solution ◽

Model Completeness ◽

Present Contribution ◽

First Order ◽

Reduction Strategies ◽

Infinite State Systems ◽

Infinite State ◽

Superposition Calculus

AbstractUniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

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