Choiceless polynomial time, counting and the Cai-Fürer-Immerman graphs

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Dawar, A; Richerby, D; Rossman, B

Published Date

  • March 1, 2008

Published In

Volume / Issue

  • 152 / 1-3

Start / End Page

  • 31 - 50

International Standard Serial Number (ISSN)

  • 0168-0072

Digital Object Identifier (DOI)

  • 10.1016/j.apal.2007.11.011

Citation Source

  • Scopus