Foundations for Decision Problems in Separation Logic with General Inductive Predicates

  • Timos Antonopoulos
  • Nikos Gorogiannis
  • Christoph Haase
  • Max Kanovich
  • Joël Ouaknine
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)

Abstract

We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment in the base language is \(\Pi_2^{\text{P}}\)-complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Timos Antonopoulos
    • 1
  • Nikos Gorogiannis
    • 2
  • Christoph Haase
    • 3
  • Max Kanovich
    • 4
  • Joël Ouaknine
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK
  2. 2.Department of Computer ScienceMiddlesex University LondonUK
  3. 3.LSVCNRS & École Normale Supérieure (ENS) de CachanFrance
  4. 4.Department of Computer ScienceQueen Mary University of LondonUK

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