A multiparametric view on answer set programming

Disjunctive answer set programming (ASP) is an important framework for declarative modeling and problem solving, where the computational complexity of basic decision problems like consistency (deciding whether a program has an answer set) is located on the second level of the polynomial hierarchy. D...

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Published in:	Annals of mathematics and artificial intelligence Vol. 86; no. 1-3; pp. 121 - 147
Main Authors:	Fichte, Johannes K., Kronegger, Martin, Woltran, Stefan
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.07.2019 Springer Springer Nature B.V
Subjects:	Algorithms Artificial Intelligence Complex Systems Complexity Computer Science Computers Consistency Declarative programming Graph representations Hardness Logic Mathematical programming Mathematics Optimization Parameterization Parameters Polynomials Problem solving Semantics Services Tightness Answer set programming (ASP) Multiparametric complexity Parameterized complexity theory Secondary 68T30, 03B42, 03B70, 68T27, 8Q15 Multi parameterizations Primary 03D15 Fixed-parameter tractability
ISSN:	1012-2443, 1573-7470
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Abstract	Disjunctive answer set programming (ASP) is an important framework for declarative modeling and problem solving, where the computational complexity of basic decision problems like consistency (deciding whether a program has an answer set) is located on the second level of the polynomial hierarchy. During the last decades different approaches have been applied to find tractable fragments of programs, in particular, also using parameterized complexity. However, the full potential of parameterized complexity has not been unlocked since only one or very few parameters have been considered at once. In this paper, we consider several natural parameters for the consistency problem of disjunctive ASP. In addition, we also take the sizes of the answer sets into account; a restriction that is particularly interesting for applications requiring small solutions as encoding subset minimization problems in ASP can be done directly due to inherent minimization in its semantics. Previous work on parameterizing the consistency problem by the size of answer sets yielded mostly negative results. In contrast, we start from recent findings for the problem WMMSAT and show several novel fixed-parameter tractability (fpt) results based on combinations of parameters. Moreover, we establish a variety of hardness results (paraNP, W[2], and W[1]-hardness) to assess tightness of our parameter combinations.
AbstractList	Disjunctive answer set programming (ASP) is an important framework for declarative modeling and problem solving, where the computational complexity of basic decision problems like consistency (deciding whether a program has an answer set) is located on the second level of the polynomial hierarchy. During the last decades different approaches have been applied to find tractable fragments of programs, in particular, also using parameterized complexity. However, the full potential of parameterized complexity has not been unlocked since only one or very few parameters have been considered at once. In this paper, we consider several natural parameters for the consistency problem of disjunctive ASP. In addition, we also take the sizes of the answer sets into account; a restriction that is particularly interesting for applications requiring small solutions as encoding subset minimization problems in ASP can be done directly due to inherent minimization in its semantics. Previous work on parameterizing the consistency problem by the size of answer sets yielded mostly negative results. In contrast, we start from recent findings for the problem WMMSAT and show several novel fixed-parameter tractability (fpt) results based on combinations of parameters. Moreover, we establish a variety of hardness results (paraNP, W[2], and W[1]-hardness) to assess tightness of our parameter combinations. Keywords Answer set programming (ASP) * Parameterized complexity theory * Multiparametric complexity * Fixed-parameter tractability * Multi parameterizations Mathematics Subject Classification (2010) Primary 03D15 * Secondary 68T30, 03B42, 03B70, 68T27, 8Q15 Disjunctive answer set programming (ASP) is an important framework for declarative modeling and problem solving, where the computational complexity of basic decision problems like consistency (deciding whether a program has an answer set) is located on the second level of the polynomial hierarchy. During the last decades different approaches have been applied to find tractable fragments of programs, in particular, also using parameterized complexity. However, the full potential of parameterized complexity has not been unlocked since only one or very few parameters have been considered at once. In this paper, we consider several natural parameters for the consistency problem of disjunctive ASP. In addition, we also take the sizes of the answer sets into account; a restriction that is particularly interesting for applications requiring small solutions as encoding subset minimization problems in ASP can be done directly due to inherent minimization in its semantics. Previous work on parameterizing the consistency problem by the size of answer sets yielded mostly negative results. In contrast, we start from recent findings for the problem WMMSAT and show several novel fixed-parameter tractability (fpt) results based on combinations of parameters. Moreover, we establish a variety of hardness results (paraNP, W[2], and W[1]-hardness) to assess tightness of our parameter combinations.
Audience	Academic
Author	Kronegger, Martin Woltran, Stefan Fichte, Johannes K.
Author_xml	– sequence: 1 givenname: Johannes K. orcidid: 0000-0002-8681-7470 surname: Fichte fullname: Fichte, Johannes K. email: johannes.fichte@tu-dresden.de organization: TU Dresden – sequence: 2 givenname: Martin surname: Kronegger fullname: Kronegger, Martin organization: Johannes Kepler University Linz, TU Wien – sequence: 3 givenname: Stefan surname: Woltran fullname: Woltran, Stefan organization: TU Wien
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Keywords	Answer set programming (ASP) Multiparametric complexity Parameterized complexity theory Secondary 68T30, 03B42, 03B70, 68T27, 8Q15 Multi parameterizations Primary 03D15 Fixed-parameter tractability
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SubjectTerms	Algorithms Artificial Intelligence Complex Systems Complexity Computer Science Computers Consistency Declarative programming Graph representations Hardness Logic Mathematical programming Mathematics Optimization Parameterization Parameters Polynomials Problem solving Semantics Services Tightness
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