Decidable Logics Combining Word Equations, Regular Expressions and Length Constraints

TL;DR

This paper introduces a decision procedure for a logic combining word equations, regular expressions, and length constraints, enabling effective satisfiability checking in complex string theories.

Contribution

It presents a novel decision procedure for quadratic word equations with regular and length constraints, reducing the problem to Presburger arithmetic and implementing an effective prototype tool.

Findings

The tool efficiently solves satisfiability problems in the combined logic.

The decision procedure is complete for the considered fragments.

Experimental results demonstrate the tool's effectiveness and efficiency.

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.