Separation Logic with One Quantified Variable

Stephane Demri (1) , Didier Galmiche (2) , Dominique Larchey-Wendling (2) , Daniel Mery (2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 TYPES - Logic, Proof Theory and Programming

We investigate first-order separation logic with one record field restricted to a unique quantified variable (1SL1). Undecidability is known when the number of quantified variables is unbounded and the satisfiability problem is PSPACE-complete for the propositional fragment. We show that the satisfiability problem for 1SL1 is PSPACE-complete and we characterize its expressive power by showing that every formula is equivalent to a Boolean combination of atomic properties. This contributes to our understanding of fragments of first-order separation logic that can specify properties about the memory heap of programs with singly-linked lists. All the fragments we consider contain the magic wand operator and first-order quantification over a single variable.

Mots clés: Separation logic; Quantifier elimination; Model Checking; Satisfiability; Computational Complexity

Domaines: Logique en informatique [cs.LO]

Stephane Demri, Didier Galmiche, Dominique Larchey-Wendling, Daniel Mery. Separation Logic with One Quantified Variable. Theory of Computing Systems, 2017, 61 (2), pp.371-461. ⟨10.1007/s00224-016-9713-1⟩. ⟨hal-01258821⟩