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Separating Rank Logic from Polynomial Time

Separating Rank Logic from Polynomial Time In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ2i cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

Separating Rank Logic from Polynomial Time

Lichter, Moritz
Journal of the ACM (JACM) , Volume 70 (2): 53 – Mar 25, 2023
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References (35)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ISSN
0004-5411
eISSN
1557-735X
DOI
10.1145/3572918
Publisher site
See Article on Publisher Site

Abstract

In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ2i cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time.

Journal

Journal of the ACM (JACM) – Association for Computing Machinery

Published: Mar 25, 2023

Keywords: Rank logic

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