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

Anuj Dawar | Zendy; David Richerby | Zendy; Benjamin Rossman | Zendy

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

Author(s) -

Anuj Dawar,

David Richerby,

Benjamin Rossman

Publication year - 2005

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2005.05.024

Subject(s) - rank (graph theory) , mathematics , extension (predicate logic) , time complexity , polynomial , constant (computer programming) , discrete mathematics , point (geometry) , combinatorics , computer science , programming language , geometry , mathematical analysis

We consider Choiceless Polynomial Time (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 C˜PT(Card), an extension of C˜PT with counting

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