no code implementations • 14 May 2018 • Johannes K. Fichte, Michael Morak, Markus Hecher, Stefan Woltran
It runs in time $O({2^{2^{k+4}} n^2})$ where k is the treewidth and n is the input size of the instance.
no code implementations • 28 Jun 2017 • Johannes K. Fichte, Markus Hecher, Irina Schindler
In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded.
1 code implementation • 28 Jun 2017 • Johannes K. Fichte, Markus Hecher, Michael Morak, Stefan Woltran
In this paper, we describe underlying concepts of our new implementation (DynASP2. 5) that shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution when solving problems as the Steiner tree problem that have been modeled in ASP on graphs with low treewidth.
1 code implementation • 9 Feb 2017 • Johannes Fichte, Markus Hecher, Michael Morak, Stefan Woltran
Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small.
no code implementations • 22 Dec 2016 • Johannes Fichte, Markus Hecher, Michael Morak, Stefan Woltran
While the solution counting problem for propositional satisfiability (#SAT) has received renewed attention in recent years, this research trend has not affected other AI solving paradigms like answer set programming (ASP).
no code implementations • 28 Nov 2018 • Johannes K. Fichte, Markus Hecher, Arne Meier
In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics.
no code implementations • 24 Jul 2019 • Mario Alviano, Carmine Dodaro, Johannes K. Fichte, Markus Hecher, Tobias Philipp, Jakob Rath
Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs.
no code implementations • 2 Oct 2019 • Johannes Klaus Fichte, Markus Hecher, Andreas Pfandler
More formally, we establish lower bounds for QSAT and treewidth, namely, that under ETH there cannot be an algorithm that solves QSAT of quantifier depth i in runtime significantly better than i-fold exponential in the treewidth and polynomial in the input size.
no code implementations • 13 Jan 2020 • Markus Hecher, Michael Morak, Stefan Woltran
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language.
no code implementations • 13 Jan 2020 • Johannes K. Fichte, Markus Hecher, Patrick Thier, Stefan Woltran
This paper deals with counting problems for instances of small treewidth.
no code implementations • 9 Jul 2020 • Markus Hecher, Jorge Fandinno
The exponential time hypothesis (ETH) implies that this result is tight for SAT, that is, SAT cannot be solved in subexponential time.
no code implementations • 5 Aug 2020 • Johannes K. Fichte, Markus Hecher, Stefan Szeider
We compare the impact of hardware advancement and algorithm advancement for SAT solving over the last two decades.
1 code implementation • 9 Nov 2020 • Johannes K. Fichte, Markus Hecher, Andre Schidler
We show that admissibility is indeed weaker than consistency and establish correctness of the DS* algorithm when using an admissible heuristic function.
no code implementations • 2 Dec 2020 • Johannes K. Fichte, Markus Hecher, Florim Hamiti
We hope that the results can be a good indicator of the current feasibility of model counting and spark many new applications.
1 code implementation • 6 Aug 2021 • Viktor Besin, Markus Hecher, Stefan Woltran
In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set.
no code implementations • 24 Aug 2022 • Markus Hecher
We present a new type of problem reduction, which is referred to by decomposition-guided (DG).
no code implementations • 7 Oct 2022 • Markus Hecher
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.
no code implementations • 18 Jan 2023 • Markus Hecher
This paper deals with a novel reduction from SAT to normal ASP that goes beyond well-known encodings: We explicitly utilize the structural power of ASP, whereby we sublinearly decrease the treewidth, which probably cannot be significantly improved.
no code implementations • 30 May 2023 • Johannes K. Fichte, Markus Hecher, Michael Morak, Patrick Thier, Stefan Woltran
Inspired by the observation that the so-called "treewidth" is one of the most prominent structural parameters, our algorithm utilizes small treewidth of the primal graph of the input instance.
no code implementations • 13 Nov 2023 • Johannes K. Fichte, Sarah Alice Gaggl, Markus Hecher, Dominik Rusovac
However, navigating through parts of the solution space requires counting many times, which is expensive in theory.
no code implementations • 5 Feb 2024 • Markus Hecher, Rafael Kiesel
Our results provide an in-depth hardness study, relying on a novel reduction from normal to disjunctive programs, trading the increase of complexity for an exponential parameter compression.