On the complexity of identifying Head Elementary Set Free programs

TL;DR

This paper proves that determining whether a logic program is head-elementary-set-free is a co-NP complete problem, resolving an open question about its computational complexity.

Contribution

It establishes the exact computational complexity of identifying head-elementary-set-free programs as co-NP complete.

Findings

The problem is co-NP complete.

It generalizes head-cycle-free programs.

Provides a complexity classification for program analysis.

Abstract

Head-elementary-set-free programs were proposed in (Gebser et al. 2007) and shown to generalize over head-cycle-free programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying head-elementary-set-free programs. This note solves the open problem, by showing that the problem is complete for co-NP.