Constraint-Based Abstract Semantics for Temporal Logic

A Direct Approach to Design and Implementation

Gourinath Banda, John Patrick Gallagher

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Abstract interpretation provides a practical approach to verifying properties of infinite-state systems. We apply the framework of abstract interpretation to derive an abstract semantic function for the modal mu-calculus, which is the basis for abstract model checking. The abstract semantic function is constructed directly from the standard concrete semantics together with a Galois connection between the concrete state-space and an abstract domain. There is no need for mixed or modal transition systems to abstract arbitrary temporal properties, as in previous work in the area of abstract model checking. Using the modal mu-calculus to implement CTL, the abstract semantics gives an over-approximation of the set of states in which an arbitrary CTL formula holds. Then we show that this leads directly to an effective implementation of an abstract model checking algorithm for CTL using abstract domains based on linear constraints. The implementation of the abstract semantic function makes use of an SMT solver. We describe an implemented system for proving properties of linear hybrid automata and give some experimental results.
Original languageEnglish
Title of host publicationLogic for Programming, Artificial Intelligence, and Reasoning : 16th International Conference, LPAR-16, Dakar, Senegal,
EditorsEdmund M. Clarke, Andrei Voronkov
Number of pages19
PublisherSpringer
Publication date30 Nov 2010
Pages27-45
ISBN (Print)978-3-642-17510-7
Publication statusPublished - 30 Nov 2010
EventInternational Conference on Logic for Programming Artificial Intelligence and Reasoning - Dakar, Senegal
Duration: 25 Apr 20101 May 2010

Conference

ConferenceInternational Conference on Logic for Programming Artificial Intelligence and Reasoning
CountrySenegal
CityDakar
Period25/04/201001/05/2010
SeriesLecture Notes in Computer Science
Volume6355
ISSN0302-9743

Cite this

Banda, G., & Gallagher, J. P. (2010). Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation. In E. M. Clarke, & A. Voronkov (Eds.), Logic for Programming, Artificial Intelligence, and Reasoning: 16th International Conference, LPAR-16, Dakar, Senegal, (pp. 27-45). Springer. Lecture Notes in Computer Science, Vol.. 6355
Banda, Gourinath ; Gallagher, John Patrick. / Constraint-Based Abstract Semantics for Temporal Logic : A Direct Approach to Design and Implementation. Logic for Programming, Artificial Intelligence, and Reasoning: 16th International Conference, LPAR-16, Dakar, Senegal,. editor / Edmund M. Clarke ; Andrei Voronkov. Springer, 2010. pp. 27-45 (Lecture Notes in Computer Science, Vol. 6355).
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abstract = "Abstract interpretation provides a practical approach to verifying properties of infinite-state systems. We apply the framework of abstract interpretation to derive an abstract semantic function for the modal mu-calculus, which is the basis for abstract model checking. The abstract semantic function is constructed directly from the standard concrete semantics together with a Galois connection between the concrete state-space and an abstract domain. There is no need for mixed or modal transition systems to abstract arbitrary temporal properties, as in previous work in the area of abstract model checking. Using the modal mu-calculus to implement CTL, the abstract semantics gives an over-approximation of the set of states in which an arbitrary CTL formula holds. Then we show that this leads directly to an effective implementation of an abstract model checking algorithm for CTL using abstract domains based on linear constraints. The implementation of the abstract semantic function makes use of an SMT solver. We describe an implemented system for proving properties of linear hybrid automata and give some experimental results.",
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Banda, G & Gallagher, JP 2010, Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation. in EM Clarke & A Voronkov (eds), Logic for Programming, Artificial Intelligence, and Reasoning: 16th International Conference, LPAR-16, Dakar, Senegal,. Springer, Lecture Notes in Computer Science, vol. 6355, pp. 27-45, Dakar, Senegal, 25/04/2010.

Constraint-Based Abstract Semantics for Temporal Logic : A Direct Approach to Design and Implementation. / Banda, Gourinath; Gallagher, John Patrick.

Logic for Programming, Artificial Intelligence, and Reasoning: 16th International Conference, LPAR-16, Dakar, Senegal,. ed. / Edmund M. Clarke; Andrei Voronkov. Springer, 2010. p. 27-45 (Lecture Notes in Computer Science, Vol. 6355).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Banda G, Gallagher JP. Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation. In Clarke EM, Voronkov A, editors, Logic for Programming, Artificial Intelligence, and Reasoning: 16th International Conference, LPAR-16, Dakar, Senegal,. Springer. 2010. p. 27-45. (Lecture Notes in Computer Science, Vol. 6355).