Affiliation:
1. TU Darmstadt, Darmstadt, Germany
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
2
i
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.
Funder
European Research Council
European Union’s Horizon 2020 research and innovation programme
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
1 articles.
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1. Compressing CFI Graphs and Lower Bounds for the Weisfeiler-Leman Refinements;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06