Computing stable models: worst-case performance estimates

TL;DR

This paper introduces improved algorithms for computing stable models of propositional logic programs, achieving better worst-case performance estimates than previous trivial bounds, especially for specific classes of programs.

Contribution

It presents new algorithms with asymptotically better worst-case performance estimates for computing stable models, including for programs with clauses of at most two literals.

Findings

Algorithms for 2-literal clause programs run in O(m×1.44225^n) time.

Derived worst-case performance bounds surpass the trivial O(m 2^n) bound.

Extended results for broader classes of logic programs.

Abstract

We study algorithms for computing stable models of propositional logic programs and derive estimates on their worst-case performance that are asymptotically better than the trivial bound of O(m 2^n), where m is the size of an input program and n is the number of its atoms. For instance, for programs, whose clauses consist of at most two literals (counting the head) we design an algorithm to compute stable models that works in time O(m\times 1.44225^n). We present similar results for several broader classes of programs, as well.