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  - 
TY  - JOUR
A1  - Fichte, Johannes Klaus
A1  - Szeider, Stefan
T1  - Backdoors to tractable answer set programming
JF  - Artificial intelligence
N2  - Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many Al problems such as reasoning in a nonmonotonic setting can be directly formulated in ASP. Although the main problems of ASP are of high computational complexity, complete for the second level of the Polynomial Hierarchy, several restrictions of ASP have been identified in the literature, under which ASP problems become tractable.
 In this paper we use the concept of backdoors to identify new restrictions that make ASP problems tractable. Small backdoors are sets of atoms that represent "clever reasoning shortcuts" through the search space and represent a hidden structure in the problem input. The concept of backdoors is widely used in theoretical investigations in the areas of propositional satisfiability and constraint satisfaction. We show that it can be fruitfully adapted to ASP. We demonstrate how backdoors can serve as a unifying framework that accommodates several tractable restrictions of ASP known from the literature. Furthermore, we show how backdoors allow us to deploy recent algorithmic results from parameterized complexity theory to the domain of answer set programming. (C) 2015 Elsevier B.V. All rights reserved.
KW  - Answer set programming
KW  - Backdoors
KW  - Computational complexity
KW  - Parameterized complexity
KW  - Kernelization
Y1  - 2015
U6  - https://doi.org/10.1016/j.artint.2014.12.001
SN  - 0004-3702
SN  - 1872-7921
VL  - 220
SP  - 64
EP  - 103
PB  - Elsevier
CY  - Amsterdam
ER  -