Compositional verification of concurrent systems by combining bisimulations

One approach to verify a property expressed as a modal μ -calculus formula on a system with several concurrent processes is to build the underlying state space compositionally (i.e., by minimizing and recomposing the state spaces of individual processes in a hierarchical way, keeping visible only th...

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Published in:Formal methods in system design Vol. 58; no. 1-2; pp. 83 - 125
Main Authors: Lang, Frédéric, Mateescu, Radu, Mazzanti, Franco
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2021
Springer Nature B.V
Springer Verlag
Subjects:
CAE) and Design
Circuits and Systems
Computer Science
Computer-Aided Engineering (CAD
Electrical Engineering
Engineering
Optimization
Software Engineering
Software Engineering/Programming and Operating Systems
Verification
Model checking
State space reduction
Modal mu-calculus
Labelled transition system
Concurrency theory
Temporal logic
temporal logic
model checking
state space reduction
labelled transition system
modal mu-calculus
ISSN:0925-9856, 1572-8102
Online Access:Get full text
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Summary:One approach to verify a property expressed as a modal μ -calculus formula on a system with several concurrent processes is to build the underlying state space compositionally (i.e., by minimizing and recomposing the state spaces of individual processes in a hierarchical way, keeping visible only the relevant actions occurring in the formula), and check the formula on the resulting state space. It was shown previously that, when checking the formulas of the L μ dbr fragment of the μ -calculus (consisting of weak modalities only), individual processes can be minimized modulo divergence-preserving branching (divbranching for short) bisimulation. In this paper, we refine this approach to handle formulas containing both strong and weak modalities, so as to enable a combined use of strong or divbranching bisimulation minimization on concurrent processes depending whether they contain or not the actions occurring in the strong modalities of the formula. We extend L μ dbr with strong modalities and show that the combined minimization approach preserves the truth value of formulas of the extended fragment. We implemented this approach on top of the CADP verification toolbox and demonstrated how it improves the capabilities of compositional verification on realistic examples of concurrent systems. In particular, we applied our approach to the verification problems of the RERS 2019 challenge and observed drastic reductions of the state space compared to the approach in which only strong bisimulation minimization is used, on formulas not preserved by divbranching bisimulation.
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ISSN:0925-9856
1572-8102
DOI:10.1007/s10703-021-00360-w