research-article

Separating Rank Logic from Polynomial Time

Author:

Moritz LichterAuthors Info & Claims

Journal of the ACM, Volume 70, Issue 2

Article No.: 14, Pages 1 - 53

https://doi.org/10.1145/3572918

Published: 25 March 2023 Publication History

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 ℤ_2ⁱ 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.

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Cited By

Dawar APago B(2024)A Logic for P: Are we Nearly There Yet?ACM SIGLOG News10.1145/3665453.366545911:2(35-60)Online publication date: 16-May-2024
https://dl.acm.org/doi/10.1145/3665453.3665459
Lichter MSchweitzer P(2024)Choiceless Polynomial Time with Witnessed Symmetric ChoiceJournal of the ACM10.1145/364810471:2(1-70)Online publication date: 12-Apr-2024
https://dl.acm.org/doi/10.1145/3648104
Collins NLevet M(2024)Count-free Weisfeiler–Leman and group isomorphismInternational Journal of Algebra and Computation10.1142/S021819672450010334:03(283-330)Online publication date: 3-Apr-2024
https://doi.org/10.1142/S0218196724500103
Show More Cited By

Index Terms

Separating Rank Logic from Polynomial Time
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity theory and logic
  2. Logic
    1. Finite Model Theory

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 70, Issue 2

April 2023

329 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3587260

Editor:
Venkatesan Guruswami
University of California, Berkeley, United States

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 March 2023

Online AM: 29 November 2022

Accepted: 19 November 2022

Revised: 15 September 2022

Received: 28 January 2022

Published in JACM Volume 70, Issue 2

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European Research Council (ERC)
European Union’s Horizon 2020 research and innovation programme

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Cited By

Dawar APago B(2024)A Logic for P: Are we Nearly There Yet?ACM SIGLOG News10.1145/3665453.366545911:2(35-60)Online publication date: 16-May-2024
https://dl.acm.org/doi/10.1145/3665453.3665459
Lichter MSchweitzer P(2024)Choiceless Polynomial Time with Witnessed Symmetric ChoiceJournal of the ACM10.1145/364810471:2(1-70)Online publication date: 12-Apr-2024
https://dl.acm.org/doi/10.1145/3648104
Collins NLevet M(2024)Count-free Weisfeiler–Leman and group isomorphismInternational Journal of Algebra and Computation10.1142/S021819672450010334:03(283-330)Online publication date: 3-Apr-2024
https://doi.org/10.1142/S0218196724500103
Grohe MLichter MNeuen DSchweitzer P(2023)Compressing CFI Graphs and Lower Bounds for the Weisfeiler-Leman Refinements2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00052(798-809)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00052

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