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Decomposing Data Structure Commutativity Proofs with \(m\!n\)-Differencing

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12597))

Abstract

Commutativity of data structure methods is of ongoing interest in contexts such as parallelizing compilers, transactional memory, speculative execution and software scalability. Despite this interest, we lack effective theories and techniques to aid commutativity verification.

In this paper, we introduce a novel decomposition to improve the task of verifying method-pair commutativity conditions from data structure implementations. The key enabling insight—called \(mn\)-differencing—defines the precision necessary for an abstraction to be fine-grained enough so that commutativity of method implementations in the abstract domain entails commutativity in the concrete domain, yet can be less precise than what is needed for full-functional correctness. We incorporate this decomposition into a proof rule, as well as an automata-theoretic reduction for commutativity verification. Finally, we discuss our simple proof-of-concept implementation and experimental results showing that \(mn\)-differencing leads to more scalable commutativity verification of some simple examples.

E. Koskinen—Supported in part by NSF award #1813745 and #2008633.

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Notes

  1. 1.

    Note: as discussed in Sect. 3, we employ the technique discussed in Sect. 4 of Bansal et al. [7] to avoid the need for under-approximation or quantifier alternation.

  2. 2.

    For example, we can use prophecy variables to translate a method such as int m(a) { if (nondet()) x := a; } into one that has does not have nondeterminism in its transition system: int m(a, rho) { if (rho) x := a; }.

  3. 3.

    https://github.com/erickoskinen/cityprover.

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Acknowledgments

We would like to thank Marco Gaboardi, Maurice Herlihy, Michael Hicks, David Naumann and the anonymous reviewers for their helpful feedback on earlier drafts of this work. This work was supported in part by NSF award #1813745 and #2008633.

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Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, USA

    Eric Koskinen

  2. Google, Inc., Menlo Park, USA

    Kshitij Bansal

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Correspondence to Eric Koskinen .

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  1. University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Koskinen, E., Bansal, K. (2021). Decomposing Data Structure Commutativity Proofs with \(m\!n\)-Differencing. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_5

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