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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Veröffentlicht in:	Annals of mathematics and artificial intelligence Jg. 86; H. 1-3; S. 121 - 147
Hauptverfasser:	Fichte, Johannes K., Kronegger, Martin, Woltran, Stefan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 01.07.2019 Springer Springer Nature B.V
Schlagworte:	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.
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Cites_doi	10.1007/978-1-4612-0515-9 10.1017/S1471068412000099 10.1007/BF01536399 10.1093/bioinformatics/11.1.49 10.1007/978-3-642-60085-2_17 10.1007/978-3-642-15025-8_24 10.1007/978-3-319-94144-8_11 10.1007/BF03037169 10.1016/j.artint.2014.12.001 10.1017/S1471068415000186 10.1007/978-3-642-40564-8_19 10.1007/BFb0023801 10.1007/978-1-4471-5559-1 10.1017/S1471068410000463 10.24963/ijcai.2017/118 10.1007/978-3-319-11558-0_12 10.1016/0743-1066(84)90014-1 10.1145/601775.601779 10.3233/SAT190014 10.1145/800133.804350 10.1609/aaai.v29i1.9662 10.1007/978-3-030-20528-7_9 10.1017/CBO9780511804090 10.1016/0304-3975(94)00251-D 10.1007/978-3-319-21275-3 10.1007/978-3-319-40970-2_4 10.1007/s00153-015-0435-x 10.1017/S1471068405002577 10.1016/S0890-5401(03)00057-9 10.1145/2480759.2480767 10.1016/S0004-3702(02)00187-X 10.1016/j.artint.2010.04.007 10.1609/aaai.v33i01.33012827 10.1016/B978-0-444-88074-1.50010-X 10.1007/978-3-642-23786-7_32 10.1007/978-3-319-77313-1_10 10.1016/j.artint.2009.10.003 10.1093/comjnl/bxm056 10.1145/2818646 10.1007/978-3-642-20832-4_8 10.1007/978-3-642-20832-4_6 10.1016/S0004-3702(02)00182-0 10.1007/978-3-319-61660-5_13 10.1007/978-3-642-14186-7_20 10.1016/S0890-5401(03)00161-5 10.1609/aaai.v28i1.9033 10.1007/3-540-45402-0_7
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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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Snippet	Disjunctive answer set programming (ASP) is an important framework for declarative modeling and problem solving, where the computational complexity of basic...
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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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