Property-directed inference of universal invariants or proving their absence

A. Karbyshev; N. Bjørner; S. Itzhaky; N. Rinetzky; S. Shoham

doi:10.1007/978-3-319-21690-4_40

Property-directed inference of universal invariants or proving their absence

A. Karbyshev^*, N. Bjørner, S. Itzhaky, N. Rinetzky, S. Shoham

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present Universal Property Directed Reachability (PDR^∀), a property-directed procedure for automatic inference of invariants in a universal fragment of first-order logic. PDR^∀ is an extension of Bradley’s PDR/IC3 algorithm for inference of propositional invariants. PDR^∀ terminates when it either discovers a concrete counterexample, infers an inductive universal invariant strong enough to establish the desired safety property, or finds a proof that such an invariant does not exist. We implemented an analyzer based on PDR^∀, and applied it to a collection of list-manipulating programs. Our analyzer was able to automatically infer universal invariants strong enough to establish memory safety and certain functional correctness properties, show the absence of such invariants for certain natural programs and specifications, and detect bugs. All this, without the need for user-supplied abstraction predicates.

Original language	English
Title of host publication	Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings
Editors	Corina S. Pasareanu, Daniel Kroening, Corina S. Pasareanu, Daniel Kroening
Publisher	Springer Verlag
Pages	583-602
Number of pages	20
ISBN (Print)	9783319216898, 9783319216898
DOIs	https://doi.org/10.1007/978-3-319-21690-4_40
State	Published - 2015
Event	27th International Conference on Computer Aided Verification, CAV 2015 - San Francisco, United States Duration: 18 Jul 2015 → 24 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9206
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Computer Aided Verification, CAV 2015
Country/Territory	United States
City	San Francisco
Period	18/07/15 → 24/07/15

Access to Document

10.1007/978-3-319-21690-4_40

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Karbyshev, A., Bjørner, N., Itzhaky, S., Rinetzky, N., & Shoham, S. (2015). Property-directed inference of universal invariants or proving their absence. In C. S. Pasareanu, D. Kroening, C. S. Pasareanu, & D. Kroening (Eds.), Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings (pp. 583-602). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9206). Springer Verlag. https://doi.org/10.1007/978-3-319-21690-4_40

Karbyshev, A. ; Bjørner, N. ; Itzhaky, S. et al. / Property-directed inference of universal invariants or proving their absence. Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings. editor / Corina S. Pasareanu ; Daniel Kroening ; Corina S. Pasareanu ; Daniel Kroening. Springer Verlag, 2015. pp. 583-602 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We present Universal Property Directed Reachability (PDR∀), a property-directed procedure for automatic inference of invariants in a universal fragment of first-order logic. PDR∀ is an extension of Bradley{\textquoteright}s PDR/IC3 algorithm for inference of propositional invariants. PDR∀ terminates when it either discovers a concrete counterexample, infers an inductive universal invariant strong enough to establish the desired safety property, or finds a proof that such an invariant does not exist. We implemented an analyzer based on PDR∀, and applied it to a collection of list-manipulating programs. Our analyzer was able to automatically infer universal invariants strong enough to establish memory safety and certain functional correctness properties, show the absence of such invariants for certain natural programs and specifications, and detect bugs. All this, without the need for user-supplied abstraction predicates.",

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Karbyshev, A, Bjørner, N, Itzhaky, S, Rinetzky, N & Shoham, S 2015, Property-directed inference of universal invariants or proving their absence. in CS Pasareanu, D Kroening, CS Pasareanu & D Kroening (eds), Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9206, Springer Verlag, pp. 583-602, 27th International Conference on Computer Aided Verification, CAV 2015, San Francisco, United States, 18/07/15. https://doi.org/10.1007/978-3-319-21690-4_40

Property-directed inference of universal invariants or proving their absence. / Karbyshev, A.; Bjørner, N.; Itzhaky, S. et al.

Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings. ed. / Corina S. Pasareanu; Daniel Kroening; Corina S. Pasareanu; Daniel Kroening. Springer Verlag, 2015. p. 583-602 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9206).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We present Universal Property Directed Reachability (PDR∀), a property-directed procedure for automatic inference of invariants in a universal fragment of first-order logic. PDR∀ is an extension of Bradley’s PDR/IC3 algorithm for inference of propositional invariants. PDR∀ terminates when it either discovers a concrete counterexample, infers an inductive universal invariant strong enough to establish the desired safety property, or finds a proof that such an invariant does not exist. We implemented an analyzer based on PDR∀, and applied it to a collection of list-manipulating programs. Our analyzer was able to automatically infer universal invariants strong enough to establish memory safety and certain functional correctness properties, show the absence of such invariants for certain natural programs and specifications, and detect bugs. All this, without the need for user-supplied abstraction predicates.

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Karbyshev A, Bjørner N, Itzhaky S, Rinetzky N , Shoham S. Property-directed inference of universal invariants or proving their absence. In Pasareanu CS, Kroening D, Pasareanu CS, Kroening D, editors, Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings. Springer Verlag. 2015. p. 583-602. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-21690-4_40

Property-directed inference of universal invariants or proving their absence

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