Logic and Computation through the Lens of Semirings
Logic in Computer Science
2025-05-21 v3 Computational Complexity
Abstract
We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order logic both in terms of a generalization of Blum-Shub-Smale machines and arithmetic circuits defined over a semiring. In particular, we give a logical characterization of constant-depth arithmetic circuits by an extension of first-order logic that holds for any semiring that is both commutative and positive.
Keywords
Cite
@article{arxiv.2502.12939,
title = {Logic and Computation through the Lens of 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:2502.12939},
year = {2025}
}