Logical Approaches to Non-deterministic Polynomial Time over Semirings
Logic in Computer Science
2025-10-01 v1
Abstract
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 Gr\"adel 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.
Cite
@article{arxiv.2509.26214,
title = {Logical Approaches to Non-deterministic Polynomial Time over Semirings},
author = {Timon Barlag and Nicolas Fröhlich and Teemu Hankala and Miika Hannula and Minna Hirvonen and Vivian Holzapfel and Juha Kontinen and Arne Meier and Laura Strieker},
journal= {arXiv preprint arXiv:2509.26214},
year = {2025}
}