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

Annals of Pure and Applied Logic 152 (1):31-50 (2008)
  Copy   BIBTEX

Abstract

We consider Choiceless Polynomial Time , 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 from image. 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 image, an extension of image with counting

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Choiceless polynomial time.Andreas Blass, Yuri Gurevich & Saharon Shelah - 1999 - Annals of Pure and Applied Logic 100 (1-3):141-187.
Addendum to “Choiceless polynomial time”.Andreas Blass, Yuri Gurevich & Saharon Shelah - 2001 - Annals of Pure and Applied Logic 112 (1):117.
On MODkP Counting Degrees.Masamitsu Ozaki & Juichi Shinoda - 1999 - Mathematical Logic Quarterly 45 (3):327-342.
Light affine lambda calculus and polynomial time strong normalization.Kazushige Terui - 2007 - Archive for Mathematical Logic 46 (3-4):253-280.
On Nondeterminism, Enumeration Reducibility and Polynomial Bounds.Kate Copestake - 1997 - Mathematical Logic Quarterly 43 (3):287-310.
The expressive power of fixed-point logic with counting.Martin Otto - 1996 - Journal of Symbolic Logic 61 (1):147-176.
A Note on The Functions Which Are Not Polynomial Time Computable From Their Graphs.Asae Mochizuki & Juichi Shinoda - 1996 - Annals of the Japan Association for Philosophy of Science 9 (1):17-21.
Machines Over the Reals and Non‐Uniformity.Felipe Cucker - 1997 - Mathematical Logic Quarterly 43 (2):143-157.
Approximate counting by hashing in bounded arithmetic.Emil Jeřábek - 2009 - Journal of Symbolic Logic 74 (3):829-860.
On the complexity of the pancake problem.Fuxiang Yu - 2007 - Mathematical Logic Quarterly 53 (4):532-546.
Polynomial time operations in explicit mathematics.Thomas Strahm - 1997 - Journal of Symbolic Logic 62 (2):575-594.

Analytics

Added to PP
2013-12-26

Downloads
19 (#682,951)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Fixed-point extensions of first-order logic.Yuri Gurevich & Saharon Shelah - 1986 - Annals of Pure and Applied Logic 32:265-280.
Choiceless polynomial time.Andreas Blass, Yuri Gurevich & Saharon Shelah - 1999 - Annals of Pure and Applied Logic 100 (1-3):141-187.
On fixed-point logic with counting.Jörg Flum & Martin Grohe - 2000 - Journal of Symbolic Logic 65 (2):777-787.

View all 6 references / Add more references