Conflict-driven answer set solving: From theory to practice

Gebser, Martin; Kaufmann, Benjamin; Schaub, Torsten

doi:10.1016/j.artint.2012.04.001

Cited by 359 publications

(394 citation statements)

References 56 publications

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“…We modified the problem by introducing additional complexities to enrich its structure and create possibilities for non-trivial modeling enhancements requiring a deeper understanding of problem properties. 4 In our experiments we aimed to understand relative advantages of sophisticated search procedures involving conflict-driven clause learning and backjumping of the ASP solver clingo versus the idea of limiting grounding and delegating some constraint solving tasks to a specialized constraint solver employed by clingcon -an idea central to CASP. We experimented with two sets of instances: a small set of 30 instances, where the integer parameters were quite small, and a large set also of 30 instances, where the integer parameters were substantially larger.…”

Section: Introductionmentioning

confidence: 99%

“…For our study we selected the highly optimized ASP system clingo 1 [4] that is based on the ASP grounder gringo [3] and the ASP solver clasp [4], and a CASP system clingcon 2 [5] that is based on modifications of gringo, clasp, and the constraint solver gecode 3 . To conduct the experiments we handcrafted a benchmark called a weighted-sequence problem.…”

Section: Introductionmentioning

confidence: 99%

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Weighted-Sequence Problem: ASP vs CASP and Declarative vs Problem-Oriented Solving

Lierler

Smith

Truszczyński

et al. 2012

Practical Aspects of Declarative Languages

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Abstract. Search problems with large variable domains pose a challenge to current answer-set programming (ASP) systems as large variable domains make grounding take a long time, and lead to large ground theories that may make solving infeasible. To circumvent the "grounding bottleneck" researchers proposed to integrate constraint solving techniques with ASP in an approach called constraint ASP (CASP). In the paper, we evaluate an ASP system clingo and a CASP system clingcon on a handcrafted problem involving large integer domains that is patterned after the database task of determining the optimal join order. We find that search methods used by clingo are superior to those used by clingcon, yet the latter system, not hampered by grounding, scales up better. The paper provides evidence that gains in solver technology can be obtained by further research on integrating ASP and CSP technologies.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weighted-Sequence Problem: ASP vs CASP and Declarative vs Problem-Oriented Solving

Lierler

Smith

Truszczyński

et al. 2012

Practical Aspects of Declarative Languages

View full text Add to dashboard Cite

show abstract

“…Assume 4 The particular encoding is 1≤i≤n+1 { n j=1 xi,j} ∪ 1≤i<i ≤n+1,1≤j≤n {¬xi,j ∨ ¬x i ,j }. 5 The intuitive idea is that the extension allows for reducing PHP n+1 n to PHP n n−1 with a polynomial number of Resolution steps.…”

Section: Pigeonhole Principle Separates Extended Asp Tableaux From Asmentioning

confidence: 99%

“…Each PHP n+1 n is unsatisfiable since there is no bijective mapping from an (n + 1)-element set to an n-element set. [23] for achieving a polynomial-length E-RES proof of a clausal encoding of the pigeonhole principle 4 , we define the polynomial size program extension…”

Section: Pigeonhole Principle Separates Extended Asp Tableaux From Asmentioning

confidence: 99%

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Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs

Järvisalo

Oikarinen

Logic Programming

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Abstract. We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in [Gebser&Schaub, ICLP 2006], with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for clause sets, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial length proof of a family of normal logic programs {Πn} for which ASP Tableaux has exponential length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the length of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.

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Balanced covering arrays: A classification of covering arrays and packing arrays via exact methods

Kampel

Hiess

Kotsireas

et al. 2023

J of Combinatorial Designs

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In this paper we investigate the intersections of classes of covering arrays (CAs) and packing arrays (PAs). The arrays appearing in these intersections obey to upper and lower bounds regarding the appearance of tuples in sub‐matrices—we call these arrays balanced covering arrays. We formulate and formalize first observations for which upper and lower bounds on the appearance of tuples it is of interest to consider these intersections of CAs and PAs. Outside of these bounds the intersections will be either empty, for the case of too restrictive constraints, or equal to the maximum element in the emerging lattices, for the case of too weak constraints. We present a column extension algorithm for classification of nonequivalent balanced CAs that uses a SAT solver or a pseudo‐Boolean (PB) solver to compute the columns suitable for array extension together with a lex‐leader ordering to identify unique representatives for each equivalence class of balanced CAs. These computations bring to light a dissection of classes of CAs that is partially nested due to the nature of the considered intersections. These dissections can be trivial, containing only a single type of balanced CAs, or can also appear as highly structured containing multiple nested types of balanced CAs. Our results indicate that balanced CAs are an interesting class of designs that is rich of structure.

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Conflict-driven answer set solving: From theory to practice

Cited by 359 publications

References 56 publications

Weighted-Sequence Problem: ASP vs CASP and Declarative vs Problem-Oriented Solving

Weighted-Sequence Problem: ASP vs CASP and Declarative vs Problem-Oriented Solving

Extended ASP Tableaux and Rule Redundancy in Normal Logic Programs

Balanced covering arrays: A classification of covering arrays and packing arrays via exact methods

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