A Practical Account into Counting Dung’s Extensions by Dynamic Programming

Dewoprabowo, Ridhwan; Fichte, Johannes Klaus; Gorczyca, Piotr Jerzy; Hecher, Markus

doi:10.1007/978-3-031-15707-3_30

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…An interesting further research direction is to study whether we can obtain better runtime results by designing algorithms that take in addition also the number (small or large) of projection arguments into account. While dynamic programming techniques have already been used for counting extensions (without projections) (Dewoprabowo, Fichte, Gorczyca, & Hecher, 2022), techniques for incremental counting (Fichte, Gaggl, Hecher, & Rusovac, 2024), massive parallelization (Fichte, Hecher, & Roland, 2021), or approximate counting (Kabir, Everardo, Shukla, Hecher, Fichte, & Meel, 2022) could be interesting for argumentation as well. Today, the best argumentation-based solvers (Niskanen & Järvisalo, 2020 rely on techniques from SAT-based solving in its core (Fichte, Berre, Hecher, & Szeider, 2023).…”

Section: Discussionmentioning

confidence: 99%

Counting Complexity for Reasoning in Abstract Argumentation

Fichte,

Hecher,

Meier

2024

jair

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In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics, including credulous reasoning. 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 the 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. Our algorithms run in double or triple exponential time in the treewidth, depending on the semantics under consideration. Finally, we establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension under the exponential time hypothesis (ETH).

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Section: Discussionmentioning

confidence: 99%

Counting Complexity for Reasoning in Abstract Argumentation

Fichte,

Hecher,

Meier

2024

jair

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“…The ASP encoding for conflict-free sets originates in the abstract argumentation system ASPARTIX (Dvořák et al 2020). More insights on counting and abstract argumentation frameworks and their varying semantics are available in the literature (Dewoprabowo et al 2022). Set (S2) consists of instances that encode a prototypical ASP domain with reachability and use of transitive closure containing cycles.…”

Section: Empirical Evaluationmentioning

confidence: 99%

IASCAR: Incremental Answer Set Counting by Anytime Refinement

FICHTE,

GAGGL,

HECHER

et al. 2024

Theory and Practice of Logic Programming

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Answer set programming (ASP) is a popular declarative programming paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If one counts under assumptions on literals, one obtains a tool to comprehend parts of the solution space, so-called answer set navigation. However, navigating through parts of the solution space requires counting many times, which is expensive in theory. Knowledge compilation compiles instances into representations on which counting works in polynomial time. However, these techniques exist only for conjunctive normal form (CNF) formulas, and compiling ASP programs into CNF formulas can introduce an exponential overhead. This paper introduces a technique to iteratively count answer sets under assumptions on knowledge compilations of CNFs that encode supported models. Our anytime technique uses the inclusion–exclusion principle to improve bounds by over- and undercounting systematically. In a preliminary empirical analysis, we demonstrate promising results. After compiling the input (offline phase), our approach quickly (re)counts.

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“…The ASP encoding for conflict-free sets originates in the abstract argumentation system ASPARTIX (Dvořák et al, 2020). More insights on counting and abstract argumentation frameworks and their varying semantics are available in the literature (Dewoprabowo et al, 2022). Set (S2) consists of instances that encode a prototypical ASP domain with reachability and use of transitive closure containing cycles.…”

Section: Empirical Evaluationmentioning

confidence: 99%

Exploiting Database Management Systems and Treewidth for Counting

Fichte¹,

Hecher²,

Thier³

et al. 2021

Theory and Practice of Logic Programming

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Bounded treewidth is one of the most cited combinatorial invariants in the literature. It was also applied for solving several counting problems efficiently. A canonical counting problem is #Sat, which asks to count the satisfying assignments of a Boolean formula. Recent work shows that benchmarking instances for #Sat often have reasonably small treewidth. This paper deals with counting problems for instances of small treewidth. We introduce a general framework to solve counting questions based on state-of-the-art database management systems (DBMSs). Our framework takes explicitly advantage of small treewidth by solving instances using dynamic programming (DP) on tree decompositions (TD). Therefore, we implement the concept of DP into a DBMS (PostgreSQL), since DP algorithms are already often given in terms of table manipulations in theory. This allows for elegant specifications of DP algorithms and the use of SQL to manipulate records and tables, which gives us a natural approach to bring DP algorithms into practice. To the best of our knowledge, we present the first approach to employ a DBMS for algorithms on TDs. A key advantage of our approach is that DBMSs naturally allow for dealing with huge tables with a limited amount of main memory (RAM).

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A Practical Account into Counting Dung’s Extensions by Dynamic Programming

Cited by 4 publications

References 11 publications

Counting Complexity for Reasoning in Abstract Argumentation

Counting Complexity for Reasoning in Abstract Argumentation

IASCAR: Incremental Answer Set Counting by Anytime Refinement

Exploiting Database Management Systems and Treewidth for Counting

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