TY  - JOUR
A1  - Hecher, Markus
T1  - Treewidth-aware reductions of normal ASP to SAT
BT  - is normal ASP harder than SAT after all?
JF  - Artificial intelligence
N2  - Answer Set Programming (ASP) is a paradigm for modeling and solving problems for knowledge representation and reasoning. There are plenty of results dedicated to studying the hardness of (fragments of) ASP. So far, these studies resulted in characterizations in terms of computational complexity as well as in fine-grained insights presented in form of dichotomy-style results, lower bounds when translating to other formalisms like propositional satisfiability (SAT), and even detailed parameterized complexity landscapes. A generic parameter in parameterized complexity originating from graph theory is the socalled treewidth, which in a sense captures structural density of a program. Recently, there was an increase in the number of treewidth-based solvers related to SAT. While there are translations from (normal) ASP to SAT, no reduction that preserves treewidth or at least keeps track of the treewidth increase is known. In this paper we propose a novel reduction from normal ASP to SAT that is aware of the treewidth, and guarantees that a slight increase of treewidth is indeed sufficient. Further, we show a new result establishing that, when considering treewidth, already the fragment of normal ASP is slightly harder than SAT (under reasonable assumptions in computational complexity). This also confirms that our reduction probably cannot be significantly improved and that the slight increase of treewidth is unavoidable. Finally, we present an empirical study of our novel reduction from normal ASP to SAT, where we compare treewidth upper bounds that are obtained via known decomposition heuristics. Overall, our reduction works better with these heuristics than existing translations. (c) 2021 Elsevier B.V. All rights reserved.
KW  - Answer set programming
KW  - Treewidth
KW  - Parameterized complexity
KW  - Complexity
KW  - analysis
KW  - Tree decomposition
KW  - Treewidth-aware reductions
Y1  - 2022
U6  - https://doi.org/10.1016/j.artint.2021.103651
SN  - 0004-3702
SN  - 1872-7921
VL  - 304
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - GEN
A1  - Fichte, Johannes Klaus
A1  - Hecher, Markus
A1  - Meier, Arne
T1  - Counting Complexity for Reasoning in Abstract Argumentation
T2  - The Thirty-Third AAAI Conference on Artificial Intelligence, the Thirty-First Innovative Applications of Artificial Intelligence Conference, the Ninth AAAI Symposium on Educational Advances in Artificial Intelligence
N2  - In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.
Y1  - 2019
SN  - 978-1-57735-809-1
SP  - 2827
EP  - 2834
PB  - AAAI Press
CY  - Palo Alto
ER  -