First-Order Logic in Finite Domains: Where Semantic Evaluation Competes with SMT Solving

TL;DR

This paper compares semantic evaluation and SMT solving for first-order formulas over finite domains in RISCAL, showing SMT generally outperforms but identifying cases where semantic evaluation is competitive, highlighting potential for improvements.

Contribution

It provides a comparative analysis of semantic evaluation and SMT solving in finite domain first-order logic, including empirical benchmarks and insights into their relative strengths.

Findings

SMT solving generally outperforms semantic evaluation

SMT solvers show significant performance variation

Certain classes of formulas favor semantic evaluation

Abstract

In this paper, we compare two alternative mechanisms for deciding the validity of first-order formulas over finite domains supported by the mathematical model checker RISCAL: first, the original approach of semantic evaluation (based on an implementation of the denotational semantics of the RISCAL language) and, second, the later approach of SMT solving (based on satisfiability preserving translations of RISCAL formulas to SMT-LIB formulas as inputs for SMT solvers). After a short presentation of the two approaches and a discussion of their fundamental pros and cons, we quantitatively evaluate them, both by a set of artificial benchmarks and by a set of benchmarks taken from real-life applications of RISCAL; for this, we apply the state-of-the-art SMT solvers Boolector, CVC4, Yices, and Z3. Our benchmarks demonstrate that (while SMT solving generally vastly outperforms semantic evaluation), the various SMT solvers exhibit great performance differences. More important, we identify classes of formulas where semantic evaluation is able to compete with (or even outperform) satisfiability solving, outlining some room for improvements in the translation of RISCAL formulas to SMT-LIB formulas as well as in the current SMT technology.