Proof spaces for unbounded parallelism

Azadeh Farzan, Zachary Kincaid, Andreas Podelski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

In this paper, we present a new approach to automatically verify multi-threaded programs which are executed by an unbounded number of threads running in parallel. The starting point for our work is the problem of how we can leverage existing automated verification technology for sequential programs (abstract interpretation, Craig interpolation, constraint solving, etc.) for multi-threaded programs. Suppose that we are given a correctness proof for a trace of a program (or for some other program fragment). We observe that the proof can always be decomposed into a finite set of Hoare triples, and we ask what can be proved from the finite set of Hoare triples using only simple combinatorial inference rules (without access to a theorem prover and without the possibility to infer genuinely new Hoare triples)? We introduce a proof system where one proves the correctness of a multi-threaded program by showing that for each trace of the program, there exists a correctness proof in the space of proofs that are derivable from a finite set of axioms using simple combinatorial inference rules. This proof system is complete with respect to the classical proof method of establishing an inductive invariant (which uses thread quantification and control predicates). Moreover, it is possible to algorithmically check whether a given set of axioms is sufficient to prove the correctness of a multi-threaded program, using ideas from well-structured transition systems.

Original languageEnglish (US)
Title of host publicationPOPL 2015 - Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
PublisherAssociation for Computing Machinery
Pages407-420
Number of pages14
ISBN (Electronic)9781450333009
DOIs
StatePublished - Jan 14 2015
Externally publishedYes
Event42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2015 - Mumbai, India
Duration: Jan 12 2015Jan 18 2015

Publication series

NameConference Record of the Annual ACM Symposium on Principles of Programming Languages
Volume2015-January
ISSN (Print)0730-8566

Other

Other42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2015
CountryIndia
CityMumbai
Period1/12/151/18/15

All Science Journal Classification (ASJC) codes

  • Software

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  • Cite this

    Farzan, A., Kincaid, Z., & Podelski, A. (2015). Proof spaces for unbounded parallelism. In POPL 2015 - Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (pp. 407-420). (Conference Record of the Annual ACM Symposium on Principles of Programming Languages; Vol. 2015-January). Association for Computing Machinery. https://doi.org/10.1145/2676726.2677012