Choiceless Polynomial Time, Counting and the Cai–Fürer–Immerman Graphs

Anuj Dawar, David Richerby, Benjamin Rossman
2006 Electronical Notes in Theoretical Computer Science  
We consider Choiceless Polynomial Time ( e 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
more » ... used, even in e CPT(Card), an extension of e CPT with counting.
doi:10.1016/j.entcs.2005.05.024 fatcat:au55aqwhandrlkdvekciabidke