BibTeX
@TECHREPORT{Beigel97closureproperties,
author = {Richard Beigel and Richard Beigel},
title = {Closure Properties of GapP and P},
institution = {},
year = {1997}
}
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Abstract
We classify the univariate functions that are relativizable closure properties of GapP, solving a problem posed by Hertrampf, Vollmer, and Wagner (Structures '95). We also give a simple proof of their classification of univariate functions that are relativizable closure properties of #P. 1. Introduction An operator H is a closure property of a class G of functions if, for all g in G, Hg belongs to G. An operator H is a relativizable closure property of a class G of functions if, for all oracles A, for all g in G A , Hg belongs to G A . Closure properties of #P and GapP, studied in [4, 5], yield important closure properties of various counting classes. Hertrampf, Vollmer, and Wagner [6] considered the special case where Hg = f ffi g for some function f of a single variable. It is known [4, 5] that #P and GapP are closed under addition and under f(n) = i n k j ; GapP is also closed under subtraction. Therefore, if a univariate function f is a linear combination of binomial coeff...
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