Extensional Uniformity for Boolean Circuits

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 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.

• Type: Conference
• Year: 2008
• Where: CSL
• Authors: Pierre McKenzie, Michael Thomas, Heribert Vollmer
• Keywords: Automated Reasoning, CSL 2008, Family Defining C, Uniformity Conditions, Uniformity Duality Property