Extensional Uniformity for Boolean Circuits

authored by

Pierre McKenzie, Michael Thomas, Heribert Vollmer

Abstract

Imposing an extensional uniformity condition on a non-uniform circuit complexity class C means simply intersecting C with a uniform class L. By contrast, the usual intensional uniformity conditions require that a resource-bounded machine be able to exhibit the circuits in the circuit family defining C. We say that (C,L) has the "Uniformity Duality Property" if the extensionally uniform class C \cap L can be captured intensionally by means of adding so-called "L-numerical predicates" to the first-order descriptive complexity apparatus describing the connection language of the circuit family defining C. This paper exhibits positive instances and negative instances of the Uniformity Duality Property.

Organisation(s)

Institute of Microbiology
Institute of Theoretical Computer Science

Type

Article

Journal

SIAM J. Comput.

Volume

39

Pages

3186-3206

No. of pages

21

Publication date

2010

Publication status

Published

Peer reviewed

Yes

Electronic version(s)

https://doi.org/10.48550/arXiv.0805.4072 (Access: Open)
https://doi.org/10.1137/080741811 (Access: Unknown)