On the Almighty Wand

Abstract : We investigate decidability, complexity and expressive power issues for (first-order) separation logic with one record field (herein called SL) and its fragments. SL can specify properties about the memory heap of programs with singly-linked lists. Separation logic with two record fields is known to be un-decidable by reduction of finite satisfiability for classical predicate logic with one binary relation. Surprisingly, we show that second-order logic is as expressive as SL and as a by-product we get undecidability of SL. This is refined by showing that SL without the separating conjunction is as expressive as SL, whence undecidable too. As a consequence, in SL the separating implication (also known as the magic wand) can simulate the separating conjunction. By contrast, we establish that SL without the magic wand is decidable, and we prove a non-elementary complexity by reduction from satisfiability for the first-order theory over finite words. This result is extended with a bounded use of the magic wand that appears in Hoare-style rules. As a generalisation, it is shown that kSL, the separation logic over heaps with k ≥ 1 record fields, is equivalent to kSO, the second-order logic over heaps with k record fields.
Type de document :
Article dans une revue
Information and Computation, Elsevier, 2012
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01905158
Contributeur : Etienne Lozes <>
Soumis le : jeudi 25 octobre 2018 - 15:53:00
Dernière modification le : mardi 13 novembre 2018 - 11:50:03

Fichier

BDL-icomp12.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01905158, version 1

Collections

Citation

Rémi Brochenin, Stephane Demri, Etienne Lozes. On the Almighty Wand. Information and Computation, Elsevier, 2012. 〈hal-01905158〉

Partager

Métriques

Consultations de la notice

1

Téléchargements de fichiers

1