Publications [#348695] of Benjamin Rossman

Papers Published

1. Dawar, A; Richerby, D; Rossman, B, Choiceless polynomial time, counting and the Cai-Fürer-Immerman graphs, Annals of Pure and Applied Logic, vol. 152 no. 1-3 (March, 2008), pp. 31-50
   (last updated on 2024/04/18)

   Abstract:
   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.