Compositional verification and 3-valued abstractions join forces

Sharon Shoham*, Orna Grumberg

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationStatic Analysis - 14th International Symposium, SAS 2007, Proceedings
PublisherSpringer Verlag
Number of pages18
ISBN (Print)9783540740605
StatePublished - 2007
Externally publishedYes
Event14th International Static Analysis Symposium, SAS 2007 - Kongens Lyngby, Denmark
Duration: 22 Aug 200724 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4634 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Static Analysis Symposium, SAS 2007
CityKongens Lyngby


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