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DOI: 10.4230/LIPIcs.FSCD.2025.13

Unifying Boolean and Algebraic Descriptive Complexity

Authors: Baptiste Chanus, Damiano Mazza, and Morgan Rogers

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

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.

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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)

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@InProceedings{chanus_et_al:LIPIcs.FSCD.2025.13,
  author =	{Chanus, Baptiste and Mazza, Damiano and Rogers, Morgan},
  title =	{{Unifying Boolean and Algebraic Descriptive Complexity}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.13},
  URN =		{urn:nbn:de:0030-drops-236286},
  doi =		{10.4230/LIPIcs.FSCD.2025.13},
  annote =	{Keywords: Descriptive complexity theory, Categorical logic, Blum-Shub-Smale complexity}
}

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Unifying Boolean and Algebraic Descriptive Complexity

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