Tractable Reasoning in a Fragment of Separation Logic

  • Byron Cook
  • Christoph Haase
  • Joël Ouaknine
  • Matthew Parkinson
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


In 2004, Berdine, Calcagno and O’Hearn introduced a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. They showed that entailment in this fragment is in coNP, but the precise complexity of this problem has been open since. In this paper, we show that the problem can actually be solved in polynomial time. To this end, we represent separation logic formulae as graphs and show that every satisfiable formula is equivalent to one whose graph is in a particular normal form. Entailment between two such formulae then reduces to a graph homomorphism problem. We also discuss natural syntactic extensions that render entailment intractable.


Normal Form Polynomial Time Black Node Separation Logic Graph Homomorphism 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Byron Cook
    • 1
    • 3
  • Christoph Haase
    • 2
  • Joël Ouaknine
    • 2
  • Matthew Parkinson
    • 1
  • James Worrell
    • 2
  1. 1.Microsoft Research CambridgeUK
  2. 2.Department of Computer ScienceUniversity of OxfordUK
  3. 3.Department of Computer ScienceQueen Mary University of LondonUK

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