A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

Abstract

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.

String Theories involving Regular Membership Predicates: From Practice to Theory and Back

“…On the other hand, this also explains the reason why in developing a practical solution for the satisfiability problem of A el formulae within our tool Z3str3RE we use many heuristics. While the result of Theorem 2 was known from [24], our approach seems to provide a deeper understanding of the hardness of this problem (and where this stems from) and of the ways we can deal with it.…”

A Decision Procedure for String Logic with Quadratic Equations, Regular Expressions and Length Constraints

“…Recently, [24,25] presents a decision procedure for subset constraints over regular expressions. [34] presents a decision procedure for regular memberships and length constraints. [22,7] presents a decidable fragment of acyclic word equations, regular expressions and constraints over length functions.…”

Unification Modulo Lists with Reverse Relation with Certain Word Equations

“…In Section 4 we show how the considerations of length of words can be built into the unification algorithms for the theories rcons and reverse. These could be of use in formal techniques based on word constraints (e.g., [2,11,17,16]) or in constraint programming [7]. Several examples are given in Section 5, to illustrate how the method we have developed in this paper operates.…”