Extensional Uniformity for Boolean Circuits

  • Authors:

  • Pierre Mckenzie;Michael Thomas;Heribert Vollmer

  • Affiliations:

  • Dép. d'informatique et de recherche opérationnelle, Université de Montréal, Montréal (Québec), Canada H3C 3J7;Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany 30167;Institut für Theoretische Informatik, Leibniz Universität Hannover, Hannover, Germany 30167

  • Venue:
  • CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
  • Year:
  • 2008

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Abstract

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