TY - GEN

T1 - Compositional verification and 3-valued abstractions join forces

AU - Shoham, Sharon

AU - Grumberg, Orna

PY - 2007

Y1 - 2007

N2 - 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 μ-calculus with respect to a given system. Given a system M = M1 ||M2, we view each component Mi as an abstraction Mi ↑ of the global system. The abstract component Mi ↑ is defined using a 3-valued semantics so that whenever a μ-calculus 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 abstraction-refinement framework, which resembles automatic Assume-Guarantee reasoning.

AB - 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 μ-calculus with respect to a given system. Given a system M = M1 ||M2, we view each component Mi as an abstraction Mi ↑ of the global system. The abstract component Mi ↑ is defined using a 3-valued semantics so that whenever a μ-calculus 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 abstraction-refinement framework, which resembles automatic Assume-Guarantee reasoning.

UR - http://www.scopus.com/inward/record.url?scp=38149052247&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74061-2_5

DO - 10.1007/978-3-540-74061-2_5

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AN - SCOPUS:38149052247

SN - 9783540740605

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 69

EP - 86

BT - Static Analysis - 14th International Symposium, SAS 2007, Proceedings

PB - Springer Verlag

T2 - 14th International Static Analysis Symposium, SAS 2007

Y2 - 22 August 2007 through 24 August 2007

ER -