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Compositional Verification and 3Valued Abstractions Join Forces
, 2007
"... Two of the most promising approaches to fighting the state explosion problem are abstraction and compositional verification. In this work we join their forces to obtain a novel fully automatic compositional technique that can determine the truth value of the full µcalculus with respect to a given s ..."
Abstract

Cited by 2 (1 self)
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Two of the most promising approaches to fighting the state explosion problem are abstraction and compositional verification. In this work we join their forces to obtain a novel fully automatic compositional technique that can determine the truth value of the full µcalculus with respect to a given system. Given a system M = M1M2, we view each component Mi as an abstraction Mi ↑ of the global system. The abstract component Mi ↑ is defined using a 3valued semantics so that whenever a µcalculus formula ϕ has a definite value (true or false) on Mi↑, the same value holds also for M. Thus, ϕ can be checked on either M1 ↑ or M2 ↑ (or both), and if any of them returns a definite result, then this result holds also for M. If both checks result in an indefinite value, the composition of the components needs to be considered. However, instead of constructing the composition of M1 ↑ and M2↑, our approach identifies and composes only the parts of the components in which their composition is necessary in order to conclude the truth value of ϕ. It ignores the parts which can be handled separately. The resulting model is often significantly smaller than the full system. We explain how our compositional approach can be combined with abstraction, in order to further reduce the size of the checked components. The result is an incremental compositional abstractionrefinement framework, which resembles automatic AssumeGuarantee reasoning.
Local abstractionrefinement for the mucalculus ⋆
"... Abstract. Counterexampleguided abstraction refinement (CEGAR) is a key technique for the verification of computer programs. Grumberg et al. developed a CEGARbased algorithm for the modal µcalculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et a ..."
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Abstract. Counterexampleguided abstraction refinement (CEGAR) is a key technique for the verification of computer programs. Grumberg et al. developed a CEGARbased algorithm for the modal µcalculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et al. is generalized by presenting a new CEGARbased algorithm for the µcalculus. It is based on a more expressive abstract model and applies refinement only locally (at a single abstract state), i.e., the lazy abstraction technique for safety properties is adapted to the µcalculus. Furthermore, it separates refinement determination from the (3valued based) model checking. Three different heuristics for refinement determination are presented and illustrated. 1
State focusing: Lazy abstraction for the mucalculus ⋆
"... Abstract. A key technique for the verification of programs is counterexampleguided abstraction refinement (CEGAR). In a previous approach, we developed a CEGARbased algorithm for the modal µcalculus, where refinement applies only locally, i.e. lazy abstraction techniques are used. Unfortunately, o ..."
Abstract
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Abstract. A key technique for the verification of programs is counterexampleguided abstraction refinement (CEGAR). In a previous approach, we developed a CEGARbased algorithm for the modal µcalculus, where refinement applies only locally, i.e. lazy abstraction techniques are used. Unfortunately, our previous algorithm was not completely lazy and had some further drawbacks, like a possible local state explosion. In this paper, we present an improved algorithm that maintains all advantages of our previous algorithm but eliminates all its drawbacks. The improvements were only possible by changing the philosophy of refinement from state splitting into the new philosophy of state focusing, where the states that are about to be split are not removed. 1