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

24 Scopus citations

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

Funding

Funders	Funder number
Broadcom Foundation
United States-Israel Binational Science Foundation
European Commission
Tel Aviv University
European Research Council	321174-VSSC
European Research Council	321174
Seventh Framework Programme	FP7/2007-2013
Seventh Framework Programme	308830
United States-Israel Binational Science Foundation	2012259

Access to Document

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

Cite this

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)).

@inproceedings{5a02820fed654bb2b80f37812cdd7521,

title = "Property-directed inference of universal invariants or proving their absence",

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.",

author = "A. Karbyshev and N. Bj{\o}rner and S. Itzhaky and N. Rinetzky and S. Shoham",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 27th International Conference on Computer Aided Verification, CAV 2015 ; Conference date: 18-07-2015 Through 24-07-2015",

year = "2015",

doi = "10.1007/978-3-319-21690-4_40",

language = "אנגלית",

isbn = "9783319216898",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "583--602",

editor = "Pasareanu, {Corina S.} and Daniel Kroening and Pasareanu, {Corina S.} and Daniel Kroening",

booktitle = "Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings",

address = "גרמניה",

}

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

TY - GEN

T1 - Property-directed inference of universal invariants or proving their absence

AU - Karbyshev, A.

AU - Bjørner, N.

AU - Itzhaky, S.

AU - Rinetzky, N.

AU - Shoham, S.

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84951159736&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-21690-4_40

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

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84951159736

SN - 9783319216898

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

SP - 583

EP - 602

BT - Computer Aided Verification - 27th International Conference, CAV 2015, Proceedings

A2 - Pasareanu, Corina S.

A2 - Kroening, Daniel

A2 - Pasareanu, Corina S.

A2 - Kroening, Daniel

PB - Springer Verlag

T2 - 27th International Conference on Computer Aided Verification, CAV 2015

Y2 - 18 July 2015 through 24 July 2015

ER -

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

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Cite this