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A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

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Frontiers of Combining Systems (FroCoS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9322))

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Abstract

We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux calculus for that fragment which uses as oracles a decision procedure for linear integer arithmetic and a number of computable functions over regular expressions. A distinguishing feature of this calculus is that it provides a completely algebraic method for solving membership constraints which can be easily integrated into multi-theory SMT solvers. Another is that it can be used to generate symbolic solutions for such constraints, that is, solved forms that provide simple and compact representations of entire sets of complete solutions. The calculus is part of a larger one providing the theoretical foundations of a high performance theory solver for string constraints implemented in the SMT solver CVC4.

This work was partially funded by NSF grants #1228765 and #1228768.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Iowa, Iowa, USA

    Tianyi Liang, Nestan Tsiskaridze & Cesare Tinelli

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Andrew Reynolds

  3. Department of Computer Science, New York University, New York, USA

    Clark Barrett

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  1. Tianyi Liang
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  2. Nestan Tsiskaridze
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  3. Andrew Reynolds
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  4. Cesare Tinelli
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  5. Clark Barrett
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Editors and Affiliations

  1. Universität Bremen, Bremen, Germany

    Carsten Lutz

  2. Fondazione Bruno Kessler, Trento, Italy

    Silvio Ranise

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Liang, T., Tsiskaridze, N., Reynolds, A., Tinelli, C., Barrett, C. (2015). A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings. In: Lutz, C., Ranise, S. (eds) Frontiers of Combining Systems. FroCoS 2015. Lecture Notes in Computer Science(), vol 9322. Springer, Cham. https://doi.org/10.1007/978-3-319-24246-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-24246-0_9

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