An Exact Characterization of Symmetric Functions in qAC0[2]

  • Chi-Jen Lu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


qAC0[2] is the class of languages computable by circuits of constant depth and quasi-polynomial \( (2^{\log ^{o(1)_{ n} } } ) \) size with unbounded fan-in AND, OR, and PARITY gates. Symmetric functions are those functions that are invariant under permutations of the input variables. Thus a symmetric function fn: 0, 1n #x2192; 0, 1 can also be seen as a function fn: 0, 1, ..., n} → 0, 1. We give the following characterization of symmetric functions in qAC0[2], according to how fn(x) changes as x grows from 0 to n. A symmetric function f = (fn) is in qAC0[2] if and only if fn has period 2t(n) = logO(1)n except within both ends of length logO(1)n.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Chi-Jen Lu
    • 1
  1. 1.Computer Science DepartmentUniversity of Massachusetts at AmherstUSA

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