Negated String Containment is Decidable

Abstract

We provide a positive answer to a long-standing open question of the decidability of the not-contains string predicate. Not-contains is practically relevant, for instance in symbolic execution of string manipulating programs. Particularly, we show that the predicate ¬Contains(x … x_n, y … y_m), where x … x_n and y … y_m are sequences of string variables constrained by regular languages, is decidable. Decidability of a not-contains predicate combined with chain-free word equations and regular membership constraints follows.We provide a positive answer to a long-standing open question of the decidability of the not-contains string predicate. Not-contains is practically relevant, for instance in symbolic execution of string manipulating programs. Particularly, we show that the predicate ¬Contains(x … x_n, y … y_m), where x … x_n and y … y_m are sequences of string variables constrained by regular languages, is decidable. Decidability of a not-contains predicate combined with chain-free word equations and regular membership constraints follows.