SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world

Solving polynomial constraints for proving termination of rewriting

A termination problem can be transformed into a set of polynomial constraints. Up to now, several approaches have been studied to deal with these constraints as constraint solving problems. In this thesis, we study in depth some of these approaches, present some advances in each approach.Navarro Marset, RA. (2008). Solving polynomial constraints for proving termination of rewriting. http://hdl.handle.net/10251/13626Archivo delegad

Generating Polynomial Orderings for Termination Proofs

Most systems for the automation of termination proofs using polynomial orderings are only semi-automatic, i.e. the "right" polynomial ordering has to be given by the user. We show that a variation of Lankford's partial derivative technique leads to an easier and slightly more powerful method than most other semi-automatic approaches. Based on this technique we develop a method for the automated synthesis of a suited polynomial ordering