Expressive Completeness of Separation Logic With Two Variables and No Separating Conjunction

Stéphane Demri (1, 2, 3) , Morgan Deters (1)

1 NYU - New York University [New York]
2 CNRS - Centre National de la Recherche Scientifique
3 LSV - Laboratoire Spécification et Vérification [Cachan]

Separation logic is used as an assertion language for Hoare-style proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak second-order logic, substantially sharpening a previous result. Capturing weak second-order logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these, and as a by-product identify the smallest fragment of separation logic known to be undecidable: first-order separation logic with one record field, two variables, and no separating conjunction. Because we forbid ourselves the use of many syntactic resources, this underscores even further the power of separating implication on concrete heaps.

Mots clés: separation logic; expressive power; magic wand; two-variable logics; undecidability; formal methods; Hoare logic

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

Stéphane Demri, Morgan Deters. Expressive Completeness of Separation Logic With Two Variables and No Separating Conjunction. ACM Transactions on Computational Logic, 2016, 17 (2), pp.12:1-12:44. ⟨10.1145/2835490⟩. ⟨hal-03186336⟩