Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $\mathbb{Z}_{2^i}$
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.

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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas