Dsat: A Native SAT Solver for Discrete Logic

TL;DR

This paper introduces Dsat, a native SAT solver designed for discrete logic variables, extending Boolean SAT solving techniques to handle variables with arbitrary values directly.

Contribution

The work presents a novel native SAT solver for discrete logic, avoiding binarization and integrating traditional SAT techniques with support for multi-valued variables.

Findings

Dsat performs competitively against CSP solvers on discrete CNFs.

It outperforms binarized SAT solvers on certain benchmarks.

Hybrid solvers are less efficient than the native approach.

Abstract

Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete variables is to binarize them into Boolean variables to allow the use of Boolean computational machinery such as SAT solvers. This technique can face both computational and semantical challenges though. In this work, we develop a native SAT solver for discrete logic, which is a direct extension of Boolean logic in which variables can take arbitrary values. Our proposed solver has a similar design to Boolean SAT solvers, with ingredients such as unit resolution and clause learning but ones that operate natively on discrete variables. We illustrate the merits of the developed SAT solver by comparing it empirically to CSP solvers applied to discrete CNFs, to Boolean SAT solver applied to binarized CNFs, and to some hybrid solvers.