Modular µ-calculus model-checking with formula-dependent hierarchical abstractions

Abstract : This paper defines a formal framework for the modular and hierarchical model-checking of µ-calculus against modular transitions systems. Given a formula ϕ, a module can be analysed alone, in such a way that the truth value of ϕ may be decided without the need to analyse other modules. If no conclusion can be drawn locally, the analysis provides information allowing to reduce the module to a smaller one that is equivalent with respect to the truth value of ϕ. This way, modules can be incrementally analysed, reduced and composed to other reduced modules until a conclusion is reached. On the one hand, modular analysis allows to avoid modules compositions and thus the corresponding combinatorial explosion; on the other hand, hierarchical analysis allows to reduce the modules that must be composed, which limits combinatorial explosion. Moreover, by proposing three complementary formula-dependent reductions, we expect better reductions than general approaches like bisimulation or τ * reductions. The current paper is focused on defining the theoretical tools for this approach; finding interesting strategies to apply them efficiently is left to future work.
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Yves-Stan Le Cornec, Franck Pommereau. Modular µ-calculus model-checking with formula-dependent hierarchical abstractions. 2014 14th International Conference on Application of Concurrency to System Design, Jun 2014, Tunis La Marsa, France. pp.11-20, ⟨10.1109/ACSD.2014.14⟩. ⟨hal-02309924⟩

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