Weighted automata and logics meet computational complexity
Complexity classes such as #P, ⊕P, GapP, OptP, NPMV, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class NP[S] for a suitable semiring S, defined via weighted Turing machines over S similarly as NP is defined in...
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| Vydané v: | Information and computation Ročník 301; s. 105213 |
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| Jazyk: | English |
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01.12.2024
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| ISSN: | 0890-5401 |
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| Abstract | Complexity classes such as #P, ⊕P, GapP, OptP, NPMV, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class NP[S] for a suitable semiring S, defined via weighted Turing machines over S similarly as NP is defined in the unweighted setting. Other complexity classes can be lifted to the quantitative world as well, the resulting classes relating to the original ones in the same way as weighted automata or logics relate to their unweighted counterparts. The article surveys these too-little-known connexions implicit in the existing literature and suggests a systematic approach to the study of weighted complexity classes. An extension of SAT to weighted propositional logic is proved to be complete for NP[S] when S is finitely generated. Moreover, a class FP[S] is introduced for each semiring S as a counterpart to P, and the relations between FP[S] and NP[S] are considered. |
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| AbstractList | Complexity classes such as #P, ⊕P, GapP, OptP, NPMV, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class NP[S] for a suitable semiring S, defined via weighted Turing machines over S similarly as NP is defined in the unweighted setting. Other complexity classes can be lifted to the quantitative world as well, the resulting classes relating to the original ones in the same way as weighted automata or logics relate to their unweighted counterparts. The article surveys these too-little-known connexions implicit in the existing literature and suggests a systematic approach to the study of weighted complexity classes. An extension of SAT to weighted propositional logic is proved to be complete for NP[S] when S is finitely generated. Moreover, a class FP[S] is introduced for each semiring S as a counterpart to P, and the relations between FP[S] and NP[S] are considered. |
| ArticleNumber | 105213 |
| Author | Kostolányi, Peter |
| Author_xml | – sequence: 1 givenname: Peter orcidid: 0000-0002-5474-8781 surname: Kostolányi fullname: Kostolányi, Peter email: kostolanyi@fmph.uniba.sk organization: Department of Computer Science, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia |
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| Keywords | Semiring Weighted Turing machine Weighted complexity class Weighted logic Completeness |
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