Tractable reasoning in a fragment of separation logic

Authors:
Byron Cook;Christoph Haase;Joël Ouaknine;Matthew Parkinson;James Worrell
Affiliations:
Microsoft Research Cambridge, UK and Department of Computer Science, Queen Mary University of London, UK;Department of Computer Science, University of Oxford, UK;Department of Computer Science, University of Oxford, UK;Microsoft Research Cambridge, UK;Department of Computer Science, University of Oxford, UK
Venue:
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Year:
2011

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Abstract

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.