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
Technical report
Publication date
27.05.2008
Publication status
Published