Logical Approaches to Non-deterministic Polynomial Time over Semirings

Fuente: arXiv
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Main Authors: Barlag, Timon, Fröhlich, Nicolas, Hankala, Teemu, Hannula, Miika, Hirvonen, Minna, Holzapfel, Vivian, Kontinen, Juha, Meier, Arne, Strieker, Laura
Format: Preprint
Published: 2025
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author Barlag, Timon
Fröhlich, Nicolas
Hankala, Teemu
Hannula, Miika
Hirvonen, Minna
Holzapfel, Vivian
Kontinen, Juha
Meier, Arne
Strieker, Laura
author_facet Barlag, Timon
Fröhlich, Nicolas
Hankala, Teemu
Hannula, Miika
Hirvonen, Minna
Holzapfel, Vivian
Kontinen, Juha
Meier, Arne
Strieker, Laura
contents We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Grädel and Tannen. Furthermore, we show that, similarly to the classical setting, the satisfiability problem of propositional logic in the semiring semantics is the canonical complete problem for this version of NP. Eventually, we prove that the true existential first-order theory of the semiring is a complete problem for the so-called Boolean part of this version of NP.
format Preprint
id arxiv_https___arxiv_org_abs_2509_26214
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Logical Approaches to Non-deterministic Polynomial Time over Semirings
Barlag, Timon
Fröhlich, Nicolas
Hankala, Teemu
Hannula, Miika
Hirvonen, Minna
Holzapfel, Vivian
Kontinen, Juha
Meier, Arne
Strieker, Laura
Logic in Computer Science
We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Grädel and Tannen. Furthermore, we show that, similarly to the classical setting, the satisfiability problem of propositional logic in the semiring semantics is the canonical complete problem for this version of NP. Eventually, we prove that the true existential first-order theory of the semiring is a complete problem for the so-called Boolean part of this version of NP.
title Logical Approaches to Non-deterministic Polynomial Time over Semirings
topic Logic in Computer Science
url https://arxiv.org/abs/2509.26214