Technical Note: Exploring \Sigma^P_2 / \Pi^P_2-hardness for Argumentation Problems with fixed distance to tractable classes

TL;DR

This paper investigates the computational complexity of reasoning in argumentation frameworks that are close to classes allowing efficient reasoning, revealing that certain problems remain hard even with structural restrictions.

Contribution

It demonstrates that reasoning problems on the second level of the polynomial hierarchy stay complex despite proximity to tractable graph classes.

Findings

Reasoning problems remain ull complexity near tractable classes.

Fixed distance to certain graph classes does not reduce problem complexity.

Complexity persists even with structural restrictions.

Abstract

We study the complexity of reasoning in abstracts argumentation frameworks close to graph classes that allow for efficient reasoning methods, i.e.\ to one of the classes of acyclic, noeven, biparite and symmetric AFs. In this work we show that certain reasoning problems on the second level of the polynomial hierarchy still maintain their full complexity when restricted to instances of fixed distance to one of the above graph classes.