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Choiceless polynomial time, counting and the Cai–Fürer–Immerman graphs (Extended Abstract) (2007)
| Venue: | IN: PROC. 12TH WORKSHOP ON LOGIC, LANGUAGE, INFORMATION AND COMPUTATION |
| Citations: | 11 - 4 self |
BibTeX
@INPROCEEDINGS{Dawar07choicelesspolynomial,
author = {Anuj Dawar and David Richerby and Benjamin Rossman},
title = {Choiceless polynomial time, counting and the Cai–Fürer–Immerman graphs (Extended Abstract)},
booktitle = {IN: PROC. 12TH WORKSHOP ON LOGIC, LANGUAGE, INFORMATION AND COMPUTATION},
year = {2007},
pages = {13--26},
publisher = {}
}
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Abstract
We consider Choiceless Polynomial Time ( ˜ CPT), 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 ˜ CPT(Card), an extension of ˜ CPT with counting.
