Deciding Entailments in Inductive Separation Logic with Tree Automata

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated verification procedure based on SL is the decidability of the entailment problem. In this work, we reduce the entailment problem for a non-trivial subset of SL describing trees (and beyond) to the language inclusion of tree automata (TA). Our reduction provides tight complexity bounds for the problem and shows that entailment in our fragment is EXPTIME-complete. For practical purposes, we leverage from recent advances in automata theory, such as inclusion checking for non-deterministic TA avoiding explicit determinization. We implemented our method and present promising preliminary experimental results

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

An Entailment Checker for Separation Logic with Inductive Definitions An Entailment Checker for Separation Logic with Inductive Definitions

International audienceIn this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formu-lae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

An Entailment Checker for Separation Logic with Inductive Definitions

In this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formulae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

Program Verification with Separation Logic

International audienceSeparation Logic is a framework for the development of modular program analyses for sequential, inter-procedural and concurrent programs. The first part of the paper introduces Separation Logic first from a historical, then from a program verification perspective. Because program verification eventually boils down to deciding logical queries such as the validity of verification conditions, the second part is dedicated to a survey of decision procedures for Separation Logic, that stem from either SMT, proof theory or automata theory. Incidentally we address issues related to decidability and computational complexity of such problems, in order to expose certain sources of intractability

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

SL-COMP: Competition of Solvers for Separation Logic

International audienceSL-COMP aims at bringing together researchers interested on improving the state of the art of the automated deduction methods for Separation Logic (SL). The event took place twice until now and collected more than 1K problems for different fragments of SL. The input format of problems is based on the SMT-LIB format and therefore fully typed; only one new command is added to SMT-LIB's list, the command for the declaration of the heap's type. The SMT-LIB theory of SL comes with ten logics, some of them being combinations of SL with linear arithmetics. The competition's divisions are defined by the logic fragment, the kind of decision problem (satisfiability or entailment) and the presence of quantifiers. Until now, SL-COMP has been run on the StarExec platform, where the benchmark set and the binaries of participant solvers are freely available. The benchmark set is also available with the competition's documentation on a public repository in GitHub