Expansion-based QBF Solving on Tree Decompositions*

Charwat, Günther; Woltran, Stefan

doi:10.3233/fi-2019-1810

Cited by 16 publications

(21 citation statements)

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“…Note that algorithm QSat t can be extended to also consider more fine-grained quantifier dependency schemes. Compared to other algorithms for QSat using treewidth [9,10], hybrid solving based on nested DP is quite compact without the need of nested tables. Instead of rather involved data structures (nested tables), we use here plain tables that can be handled by modern database systems efficiently.…”

Section: Hybrid Solving Based On Nested Dpmentioning

confidence: 99%

“…For several problems hard for complexity class NP, there are results [12] showing socalled (fixed-parameter) tractability, which indicates a fixed-parameter tractable (FPT) algorithm running in polynomial time assuming that a given parameter (e.g., treewidth) is fixed. Practical implementations exploiting treewidth include generic frameworks [3,5,36], but also dedicated solvers that deal with problems ranging from (counting variants of) Boolean satisfiability (Sat) [25], over generalizations thereof [9,10] based on Quantified Boolean Formulas (QBFs), to formalisms relevant to knowledge representation and reasoning [22]. For Sat, these solvers are of particular interest as there is a well-known correspondence between treewidth and resolution width [2].…”

Section: Introductionmentioning

confidence: 99%

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Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology

Hecher

Thier

Woltran

2020

Lecture Notes in Computer Science

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Treewidth is one of the most prominent structural parameters. While numerous theoretical results establish tractability under the assumption of fixed treewidth, the practical success of exploiting this parameter is far behind what theoretical runtime bounds have promised. In particular, a naive application of dynamic programming (DP) on tree decompositions (TDs) suffers already from instances of medium width. In this paper, we present several measures to advance this paradigm towards general applicability in practice: We present nested DP, where different levels of abstractions are used to (recursively) compute TDs of a given instance. Further, we integrate the concept of hybrid solving, where subproblems hidden by the abstraction are solved by classical search-based solvers, which leads to an interleaving of parameterized and classical solving. Finally, we provide nested DP algorithms and implementations relying on database technology for variants and extensions of Boolean satisfiability. Experiments indicate that the advancements are promising.

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Section: Hybrid Solving Based On Nested Dpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology

Hecher

Thier

Woltran

2020

Lecture Notes in Computer Science

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“…This observation gives rise to a general framework for counting problems that leverages treewidth. The general idea to develop such frameworks is indeed not new, since there are both, specialized solvers [9,23,25], as well as general systems like D-FLAT [5], Jatatosk [4], and sequoia [31], that exploit treewidth. Some of these systems explicitly use dynamic programming (DP) to directly exploit treewidth by means of so-called tree decompositions (TDs), whereas others provide some kind of declarative layer to model the problem (and perform decomposition and DP internally).…”

Section: Introductionmentioning

confidence: 99%

Exploiting Database Management Systems and Treewidth for Counting

Fichte

Hecher

Thier

et al. 2020

Lecture Notes in Computer Science

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Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature 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 (DBMS). 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 DBMS naturally allow to deal with huge tables with a limited amount of main memory (RAM), parallelization, as well as suspending computation.

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“…It turns out that this question can be answered in the affirmative: the main decision problems become tractable. In practice, a dynamic programming algorithm on tree decompositions can be used to exploit this directly, similarly to what was successfully proposed for ASP and QBF solvers [4,8,15,17]. However, we also aim to investigate a more interesting angle.…”

Section: Introductionmentioning

confidence: 99%

Structural Decompositions of Epistemic Logic Programs

Hecher¹,

Morak²,

Woltran³

2020

Preprint

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Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational complexity reaching up to the fourth level of the polynomial hierarchy. However, in contrast to standard ASP, dedicated investigations towards tractability have not been undertaken yet. In this paper, we give first results in this direction and show that central ELP problems can be solved in linear time for ELPs exhibiting structural properties in terms of bounded treewidth. We also provide a full dynamic programming algorithm that adheres to these bounds. Finally, we show that applying treewidth to a novel dependency structure-given in terms of epistemic literals-allows to bound the number of ASP solver calls in typical ELP solving procedures.

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Expansion-based QBF Solving on Tree Decompositions*

Cited by 16 publications

References 0 publications

Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology

Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology

Exploiting Database Management Systems and Treewidth for Counting

Structural Decompositions of Epistemic Logic Programs

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