### Abstract

In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of words. We present a novel decision procedure over two decidable fragments that include quadratic word equations (i.e., each string variable occurs at most twice). The proposed procedure reduces the problem to solving the satisfiability in the Presburger arithmetic. The procedure combines two main components: (i) an algorithm to derive a complete set of all solutions of conjunctions of word equations and regular expressions; and (ii) two methods to precisely compute relational constraints over string lengths implied by the set of all solutions. We have implemented a prototype tool and evaluated it over a set of satisfiability problems in the logic. The experimental results show that the tool is effective and efficient.

Original language | English |
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Publication status | Accepted/In press - 13 Aug 2018 |

Event | 16th Asian Symposium on Programming Languages and Systems - Wellington, New Zealand Duration: 3 Dec 2018 → 5 Dec 2018 http://aplas2018.org |

### Conference

Conference | 16th Asian Symposium on Programming Languages and Systems |
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Abbreviated title | APLAS 2018 |

Country | New Zealand |

City | Wellington |

Period | 3/12/18 → 5/12/18 |

Internet address |

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## Cite this

Le, Q. L., & He, M. (Accepted/In press).

*A Decision Procedure for String Logic with Quadratic Equations, Regular Expressions and Length Constraints*. Paper presented at 16th Asian Symposium on Programming Languages and Systems, Wellington, New Zealand.