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 Property if the extensionally uniform class \(\mathcal{C}\cap\mathcal{L}\) can be captured intensionally by means of adding so-called \(\mathcal{L}\) -numerical predicates to 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.
Supported in part by DFG VO 630/6-1, by the NSERC of Canada and by the (Québec) FQRNT.
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McKenzie, P., Thomas, M., Vollmer, H. (2008). Extensional Uniformity for Boolean Circuits. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_7
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DOI: https://doi.org/10.1007/978-3-540-87531-4_7
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