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International Conference on Automated Deduction

CADE 2017: Automated Deduction – CADE 26 pp 472–490Cite as

Biabduction (and Related Problems) in Array Separation Logic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

Abstract

We investigate array separation logic (\(\mathsf {ASL}\)), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \(\mathsf {NP}\) decision procedure for biabduction in \(\mathsf {ASL}\), and we also show that the problem of finding a consistent solution is \(\mathsf {NP}\)-hard. Along the way, we study satisfiability and entailment in \(\mathsf {ASL}\), giving decision procedures and complexity bounds for both problems. We show satisfiability to be \(\mathsf {NP}\)-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space.

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Author information

Authors and Affiliations

  1. University College London, London, UK

    James Brotherston & Max Kanovich

  2. Middlesex University, London, UK

    Nikos Gorogiannis

  3. National Research University Higher School of Economics, Moscow, Russian Federation

    Max Kanovich

Authors
  1. James Brotherston
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  2. Nikos Gorogiannis
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  3. Max Kanovich
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Correspondence to James Brotherston .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Brotherston, J., Gorogiannis, N., Kanovich, M. (2017). Biabduction (and Related Problems) in Array Separation Logic. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_29

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_29

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