Choiceless Polynomial Time, Counting and the Cai-Fürer-Immerman Graphs: (Extended Abstract)

Abstract We consider Choiceless Polynomial Time ( C PT ), a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Furer 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 used, even in C PT(Card) , an extension of C PT with counting.

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