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.
Recently, the entailment problem for SLRD over lists has been reduced to graph homomorphism in REF , and can be solved in PTIME.
Tractable reasoning in a fragment of separation logic
In 22nd CONCUR, Springer LNCS 6901
Computer Science