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arXiv · 0805.4072

Extensional Uniformity for Boolean Circuits

Pierre McKenzie·Michael Thomas·Heribert Vollmer
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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.

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Pierre McKenzie, Michael Thomas, Heribert Vollmer. 2008-05-28. Extensional Uniformity for Boolean Circuits. https://arxiv.org/abs/0805.4072

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