Implementing a Relevance Tracker Module

TL;DR

This paper presents an incremental relevance tracker module for PC(ID) solvers, enabling more efficient decision-making by focusing only on relevant literals during the search process.

Contribution

It introduces a lightweight, incremental relevance tracker that interacts with existing SAT(ID) solvers, improving their efficiency by dynamically identifying relevant literals.

Findings

The relevance tracker accurately identifies relevant literals during solver search.

The module can be integrated with existing solvers without significant overhead.

Relevance tracking improves solver performance by reducing unnecessary decisions.

Abstract

PC(ID) extends propositional logic with inductive definitions: rule sets under the well-founded semantics. Recently, a notion of relevance was introduced for this language. This notion determines the set of undecided literals that can still influence the satisfiability of a PC(ID) formula in a given partial assignment. The idea is that the PC(ID) solver can make decisions only on relevant literals without losing soundness and thus safely ignore irrelevant literals. One important insight that the relevance of a literal is completely determined by the current solver state. During search, the solver state changes have an effect on the relevance of literals. In this paper, we discuss an incremental, lightweight implementation of a relevance tracker module that can be added to and interact with an out-of-the-box SAT(ID) solver.