### 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 language | English (US) |
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Title of host publication | Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings |

Publisher | Springer Verlag |

Pages | 135-150 |

Number of pages | 16 |

Volume | 9322 |

ISBN (Print) | 9783319242453 |

DOIs | |

State | Published - 2015 |

Event | 10th International Symposium on Frontiers of Combining Systems, FroCoS 2015 - Wroclaw, Poland Duration: Sep 21 2015 → Sep 24 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9322 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Symposium on Frontiers of Combining Systems, FroCoS 2015 |
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Country | Poland |

City | Wroclaw |

Period | 9/21/15 → 9/24/15 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings*(Vol. 9322, 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

**A decision procedure for regular membership and length constraints over unbounded strings.** / Liang, Tianyi; Tsiskaridze, Nestan; Reynolds, Andrew; Tinelli, Cesare; Barrett, Clark.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings.*vol. 9322, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9322, Springer Verlag, pp. 135-150, 10th International Symposium on Frontiers of Combining Systems, FroCoS 2015, Wroclaw, Poland, 9/21/15. https://doi.org/10.1007/978-3-319-24246-0_9

}

TY - GEN

T1 - A decision procedure for regular membership and length constraints over unbounded strings

AU - Liang, Tianyi

AU - Tsiskaridze, Nestan

AU - Reynolds, Andrew

AU - Tinelli, Cesare

AU - Barrett, Clark

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84950117776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950117776&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-24246-0_9

DO - 10.1007/978-3-319-24246-0_9

M3 - Conference contribution

SN - 9783319242453

VL - 9322

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 135

EP - 150

BT - Frontiers of Combining Systems - 10th International Symposium, FroCoS 2015, Proceedings

PB - Springer Verlag

ER -