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Choiceless Polynomial Time, Counting and the Cai–Fürer–Immerman Graphs
<span title="">2006</span>
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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a>
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We consider Choiceless Polynomial Time ( e CPT), a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate fixed-point logic with counting (IFP + C) from P. This settles a question posed by Blass et al. The program we present uses sets of unbounded finite rank: we demonstrate that this is necessary by showing that the query cannot be computed by any program that has a constant bound on the rank of sets
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... used, even in e CPT(Card), an extension of e CPT with counting.
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