A decision procedure for regular membership and length constraints over unbounded strings

Tianyi Liang, Nestan Tsiskaridze, Andrew Reynolds, Cesare Tinelli, Clark Barrett

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

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.

Original languageEnglish (US)
Title of host publicationFrontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings
EditorsCarsten Lutz, Silvio Ranise
PublisherSpringer Verlag
Pages135-150
Number of pages16
ISBN (Print)9783319242453
DOIs
StatePublished - Jan 1 2015
Event10th International Symposium on Frontiers of Combining Systems, FroCoS 2015 - Wroclaw, Poland
Duration: Sep 21 2015Sep 24 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9322
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Symposium on Frontiers of Combining Systems, FroCoS 2015
CountryPoland
CityWroclaw
Period9/21/159/24/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Liang, T., Tsiskaridze, N., Reynolds, A., Tinelli, C., & Barrett, C. (2015). A decision procedure for regular membership and length constraints over unbounded strings. In C. Lutz, & S. Ranise (Eds.), Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings (pp. 135-150). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9322). Springer Verlag. https://doi.org/10.1007/978-3-319-24246-0_9