Choiceless polynomial time, counting and the cai-fürer-immerman graphs: (Extended abstract)

We consider Choiceless Polynomial Time (C̃PT), 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 C̃PT(Card), an extension of C̃PT with counting. © 2005 Elsevier B.V. All rights reserved.

Duke Scholars

Author Benjamin Rossman Computer Science