Local Search for SMT on Linear Integer Arithmetic

Abstract

Satisfiability Modulo Linear Integer Arithmetic, SMT (LIA) for short, has significant applications in many domains. In this paper, we develop the first local search algorithm for SMT (LIA) by directly operating on variables, breaking through the traditional framework. We propose a local search framework by considering the distinctions between Boolean and integer variables. Moreover, we design a novel operator and scoring functions tailored for LIA, and propose a two-level operation selection heuristic. Putting these together, we develop a local search SMT (LIA) solver called LS-LIA. Experiments are carried out to evaluate LS-LIA on benchmarks from SMTLIB and two benchmark sets generated from job shop scheduling and data race detection. The results show that LS-LIA is competitive and complementary with state-of-the-art SMT solvers, and performs particularly well on those formulae with only integer variables. A simple sequential portfolio with Z3 improves the state-of-the-art on satisfiable benchmark sets of LIA and IDL benchmarks from SMT-LIB. LS-LIA also solves Job Shop Scheduling benchmarks substantially faster than traditional complete SMT solvers.