A symbolic algorithm for the case-split rule in solving word constraints with extensions

• Published in: The Journal of systems and software Vol. 201; p. 111673
• Main Authors: Chen, Yu-Fang, Havlena, Vojtěch, Lengál, Ondřej, Turrini, Andrea
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2023
• Subjects: Finite automata; Monadic second-order logic over strings; Nielsen transformation; Regular model checking; Satisfiability modulo theories; String constraints; Monadic second-order logic over strings; Regular model checking; String constraints; Satisfiability modulo theories; Finite automata; Nielsen transformation
• ISSN: 0164-1212; 1873-1228
• DOI: 10.1016/j.jss.2023.111673

Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in the proof tree. Moreover, explicit handling of the case split rule may cause recomputation of the same tasks in multiple branches of the proof tree. In this paper, we propose a symbolic algorithm that significantly reduces such a redundancy. In particular, we encode a string constraint as a regular language and proof rules as rational transducers. This allows us to perform similar steps in the proof tree only once, alleviating the state space explosion. We also extend the encoding to handle arbitrary Boolean combinations of string constraints, length constraints, and regular constraints. In our experimental results, we validate that our technique works in many practical cases where other state-of-the-art solvers fail to provide an answer; our Python prototype implementation solved over 50% of string constraints that could not be solved by the other tools. •Solving string constraints using regular model checking.•Nielsen transformation using automata and transducers.•Compact encoding of the generated state space.•Provides significant advantage on hard formulae.