Breaking Symmetries with RootClique and LexTopSort

Fichte, Johannes Klaus; Hecher, Markus; Szeider, Stefan

doi:10.1007/978-3-030-58475-7_17

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…While the (fractional) hypertree width subsumes treewidth, there are even dedicated tools for computing such decompositions efficiently, cf. [Gottlob and Samer, 2009;Fichte et al, 2018a;Korhonen et al, 2019;Fischl et al, 2019;Fichte et al, 2020f].…”

Section: Related Workmentioning

confidence: 99%

Advanced tools and methods for treewidth-based problem solving

Hecher¹

2023

It - Information Technology

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Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula’s structural properties during solving. One of such structural indicators is the so-called treewidth, which tries to measure how close a formula instance is to being easy (tree-like). This work focuses on logic-based problems and treewidth-based methods and tools for solving them. Many of these problems are also relevant for knowledge representation and reasoning (KR) as well as artificial intelligence (AI) in general. We present a new type of problem reduction, which is referred to by decomposition-guided (DG). This reduction type forms the basis to solve a problem for quantified Boolean formulas (QBFs) of bounded treewidth that has been open since 2004. The solution of this problem then gives rise to a new methodology for proving precise lower bounds for a range of further formalisms in logic, KR, and AI. Despite the established lower bounds, we implement an algorithm for solving extensions of Sat efficiently, by directly using treewidth. Our implementation is based on finding abstractions of instances, which are then incrementally refined in the process. Thereby, our observations confirm that treewidth is an important measure that should be considered in the design of modern solvers.

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Section: Related Workmentioning

confidence: 99%

Advanced tools and methods for treewidth-based problem solving

Hecher¹

2023

It - Information Technology

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“…Let ≤ * be an arbitrary total order on the vertices of G. The canonical topological sort of G is the topological sort that results from always picking the greatest source vertex under ≤ * . The idea for this symmetry breaking is due to Schidler and Szeider (2020) who introduced it in a different context; Fichte, Hecher, and Szeider (2020) further studied this technique under the name LexTopSort.…”

Section: Symmetry Breakingmentioning

confidence: 99%

Finding the Hardest Formulas for Resolution

Peitl

Szeider

2021

jair

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A CNF formula is harder than another CNF formula with the same number of clauses if it requires a longer resolution proof. In this paper we introduce resolution hardness numbers; they give for m=1,2,... the length of a shortest proof of a hardest formula on m clauses. We compute the first ten resolution hardness numbers, along with the corresponding hardest formulas. To achieve this, we devise a candidate filtering and symmetry breaking search scheme for limiting the number of potential candidates for hardest for- mulas, and an efficient SAT encoding for computing a shortest resolution proof of a given candidate formula.

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