Pushing the envelope of Optimization Modulo Theories with Linear-Arithmetic Cost Functions

TL;DR

This paper advances Optimization Modulo Theories by extending its capabilities to mixed integer/rational domains, multi-objective optimization, and incremental solving, demonstrating improved efficiency on verification problems.

Contribution

It introduces three key extensions to OMT: handling mixed integer/rational domains, multi-objective optimization, and incremental solving, enhancing its applicability and performance.

Findings

Effective handling of mixed integer/rational domains.

Successful multi-objective optimization in OMT.

Demonstrated efficiency improvements on verification benchmarks.

Abstract

In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art SMT solvers, in particular in the domain of SW and HW verification. Many SMT-encodable problems of interest, however, require also the capability of finding models that are optimal wrt. some cost functions. In previous work, namely "Optimization Modulo Theory with Linear Rational Cost Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the minimization of cost functions on linear arithmetic over the rationals, by means of a combination of SMT and LP minimization techniques. In this paper we push the envelope of our OMT approach along three directions: first, we extend it to work also with linear arithmetic on the mixed integer/rational domain, by means of a combination of SMT, LP and ILP minimization techniques; second, we develop a multi-objective version of OMT, so that to handle many cost functions simultaneously; third, we develop an incremental version of OMT, so that to exploit the incrementality of some OMT-encodable problems. An empirical evaluation performed on OMT-encoded verification problems demonstrates the usefulness and efficiency of these extensions.