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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Bibliographic Details
Published in:Information and computation Vol. 301; p. 105213
Main Author: Kostolányi, Peter
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2024
Subjects:
Completeness
Semiring
Weighted complexity class
Weighted logic
Weighted Turing machine
Semiring
Weighted Turing machine
Weighted complexity class
Weighted logic
Completeness
ISSN:0890-5401
Online Access:Get full text
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Summary: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.
ISSN:0890-5401
DOI:10.1016/j.ic.2024.105213