Speeding up the Constraint-Based Method in Difference Logic

Abstract

Abstract. Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u − v ≤ k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas' Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification system.

From MiniZinc to Optimization Modulo Theories, and Back (Extended Version)

“…To this aim, we observe that (i) some of these solvers are quite recent, (ii) most of these solvers focus on different, partially overlapping, niche subsets of Optimization Modulo Theories, and (iii) the lack of an official Input/Output interface for OMT makes it hard to compare some of these tools with one another. OMT finds applications in the context of static analysis [20,32], formal verification and model checking [37,48], scheduling and planning with resources [33,35,50,46], software security and requirements engineering [41], workflow analysis [14], machine learning [59], and quantum computing [15]. Remark 1.…”