ProVal

This paper describes a novel decision procedure for quantifier-free linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g. Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaustive search for a model with bounds inference. These bounds are computed provided an oracle capable of finding constant positive linear combinations of affine forms. We also show how to design an efficient oracle based on the Simplex procedure. Our algorithm is proved sound, complete, and terminating and is implemented in the Alt-Ergo theorem prover. Experimental results are promising and show that our approach is competitive with state-of-the-art SMT solvers.

Why3 is the next generation of the Why software verification platform. Why3 clearly separates the purely logical specification part from generation of verification conditions for programs. This article focuses on the former part. Why3 comes with a new enhanced language of logical specification. It features a rich library of proof task transformations that can be chained to produce a suitable input for a large set of theorem provers, including SMT solvers, TPTP provers, as well as interactive proof assistants.

We describe an algorithm to disprove entailment between separation logic formulas. We abstract models of formulas by their size and check whether two formulas have models whose sizes are compatible. Given two formulas A and B that do not have compatible models, we can conclude that A does not entail B. We provide two different abstractions (of different precision) of models. Our algorithm is of interest wherever entailment checking is performed (such as in program verifiers).