Two-Variable Separation Logic and Its Inner Circle

Stéphane Demri (1, 2) , Morgan Deters (1)

1 NYU - New York University [New York]
2 CNRS - Centre National de la Recherche Scientifique

Separation logic is a well-known assertion language for Hoare-style proof systems. We show that first-order separation logic with a unique record field restricted to two quantified variables and no program variables is undecidable. This is among the smallest fragments of separation logic known to be undecidable, and this contrasts with decidability of two-variable first-order logic. We also investigate its restriction by dropping the magic wand connective, known to be decidable with non-elementary complexity, and we show that the satisfiability problem with only two quantified variables is not yet elementary recursive. Furthermore, we establish insightful and concrete relationships between two-variable separation logic and propositional interval temporal logic (PITL), data logics, and modal logics, providing an inner circle of closely-related logics.

Mots clés: complexity; decidability; data logic; modal logic; interval temporal logic; two-variable logic; separation logic; Minsky machine; modal separation logic; magic wand; undecidability

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri, Morgan Deters. Two-Variable Separation Logic and Its Inner Circle. ACM Transactions on Computational Logic, 2015, 16 (2:15), ⟨10.1145/2724711⟩. ⟨hal-03192209⟩