On the Complexity of the Discussion-based Semantics in Abstract Argumentation

TL;DR

This paper proves that determining argument strength under discussion-based semantics is polynomial-time decidable by relating it to automata theory and graph walk counts.

Contribution

It introduces a novel automata-theoretic approach to analyze the complexity of discussion-based semantics in abstract argumentation.

Findings

Deciding argument strength is polynomial-time decidable.

The problem reduces to automata equivalence and graph walk counting.

Provides new insights into the computational complexity of ranking semantics.

Abstract

We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two vertices in a graph, the number of walks of each length ending in those vertices is the same. We employ results from automata theory and reduce this problem to the equivalence problem for semiring automata. This offers a new perspective on the computational complexity of ranking semantics, an area in which the complexity of many semantics remains open.