Choiceless polynomial time, counting and the Cai-Fürer-Immerman graphs
We consider Choiceless Polynomial Time (over(C, ̃) PT), 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 used, even in over(C, ̃) PT(Card), an extension of over(C, ̃) PT with counting. © 2007 Elsevier B.V. All rights reserved.
Dawar, A; Richerby, D; Rossman, B
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