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Unifying Boolean and Algebraic Descriptive Complexity

Authors Baptiste Chanus , Damiano Mazza , Morgan Rogers

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Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Complexity classes
  • Theory of computation → Finite Model Theory
Keywords
  • Descriptive complexity theory
  • Categorical logic
  • Blum-Shub-Smale complexity

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Abstract

We introduce ultrarings, which simultaneously generalize commutative rings and Boolean lextensive categories. As such, they allow to blend together standard algebraic notions (from commutative algebra) and logical notions (from categorical logic), providing a unifying descriptive framework in which complexity classes over arbitrary rings (as in the Blum, Schub, Smale model) and usual, Boolean complexity classes may be captured in a uniform way.

Cite As Get BibTex

Baptiste Chanus, Damiano Mazza, and Morgan Rogers. Unifying Boolean and Algebraic Descriptive Complexity. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSCD.2025.13

Author Details

Baptiste Chanus
  • Université Sorbonne Paris Nord, LIPN, CNRS, Villetaneuse, France
Damiano Mazza
  • CNRS, LIPN, Université Sorbonne Paris Nord, Villetaneuse, France
Morgan Rogers
  • Université Sorbonne Paris Nord, LIPN, CNRS, Villetaneuse, France

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