A Fine-Grained Complexity View on Propositional Abduction - Algorithms and Lower Bounds
Victor Lagerkvist, Mohamed Maizia, Johannes Schmidt
Abstract
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning, e.g., abductive reasoning, comparably little is known outside classic complexity theory. In this paper we take a first step of bridging the gap between monotonic and non-monotonic reasoning by analyzing the complexity of intractable abduction problems under the seemingly overlooked but natural parameter n: the number of variables in the knowledge base. We obtain several positive results for SigmaP2- as well as NP- and coNP-complete fragments, which implies the first example of beating exhaustive search for a SigmaP2-complete problem (to the best of our knowledge). We complement this with lower bounds and for many fragments rule out improvements under the (strong) exponential-time hypothesis.
BibTeX
@inproceedings{ijcai2025_afinegrainedcomp,
title = {A Fine-Grained Complexity View on Propositional Abduction - Algorithms and Lower Bounds},
author = {Victor Lagerkvist and Mohamed Maizia and Johannes Schmidt},
booktitle = {IJCAI 2025},
year = {2025}
}