Biabduction (and related problems) in array separation logic

We investigate array separation logic (\mathsf {ASL}), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \mathsf {NP} decision procedure for biabduction in \mathsf {ASL}, and we also show that the problem of finding a consistent solution is \mathsf {NP}-hard. Along the way, we study satisfiability and entailment in \mathsf {ASL}, giving decision procedures and complexity bounds for both problems. We show satisfiability to be \mathsf {NP}-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space

Biabduction (and related problems) in array separation logic

We investigate array separation logic (\mathsf {ASL}), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \mathsf {NP} decision procedure for biabduction in \mathsf {ASL}, and we also show that the problem of finding a consistent solution is \mathsf {NP}-hard. Along the way, we study satisfiability and entailment in \mathsf {ASL}, giving decision procedures and complexity bounds for both problems. We show satisfiability to be \mathsf {NP}-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space

Decision Procedure for Entailment of Symbolic Heaps with Arrays

This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays in the succedent are not existentially bound. This condition is independent of the condition proposed by the CADE-2017 paper by Brotherston et al, namely, one of them does not imply the other. For improving efficiency of the decision procedure, some techniques are also presented. The main idea of the decision procedure is a novel translation of an entailment of symbolic heaps into a formula in Presburger arithmetic, and to combine it with an external SMT solver. This paper also gives experimental results by an implementation, which shows that the decision procedure works efficiently enough to use

Compositional Satisfiability Solving in Separation Logic

We introduce a novel decision procedure to the satisfiability problem in array separation logic combined with general inductively defined predicates and arithmetic. Our proposal differentiates itself from existing works by solving satisfiability through compositional reasoning. First, following Fermat’s method of infinite descent, it infers for every inductive definition a “base” that precisely characterises the satisfiability. It then utilises the base to derive such a base for any formula where these inductive predicates reside in. Especially, we identify an expressive decidable fragment for the compositionality. We have implemented the proposal in a tool and evaluated it over challenging problems. The experimental results show that the compositional satisfiability solving is efficient and our tool is effective and efficient when compared with existing solvers

Tractability of Separation Logic with Inductive Definitions: Beyond Lists

In 2011, Cook et al. showed that the satisfiability and entailment can be checked in polynomial time for a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. In this paper, we investigate whether the tractability results can be extended to more expressive fragments of separation logic that allow defining data structures beyond linked lists. To this end, we introduce separation logic with a simply-nonlinear compositional inductive predicate where source, destination, and static parameters are identified explicitly (SLID[snc]). We show that if the inductive predicate has more than one source (destination) parameter, the satisfiability problem for SLID[snc] becomes intractable in general. This is exemplified by an inductive predicate for doubly linked list segments. By contrast, if the inductive predicate has only one source (destination) parameter, the satisfiability and entailment problems for SLID[snc] are tractable. In particular, the tractability results hold for inductive predicates that define list segments with tail pointers and trees with one hole