On the expressibility of stochastic switching circuits

Authors:
Hongchao Zhou;Jehoshua Bruck
Affiliations:
Department of Electrical Engineering, California Institute of Technology, Pasadena, CA;Department of Electrical Engineering, California Institute of Technology, Pasadena, CA
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Year:
2009

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Abstract

Stochastic switching circuits are relay circuits that consist of stochastic switches (that we call pswitches). We study the expressive power of these circuits; in particular, we address the following basic question: given an arbitrary integer q, and a pswitch set {1/q, 2/q, ...., q-1/q}, can we realize any rational probability with dencimlnator qn (for arbitrary n) by a simple series-parallel stochastic switching circuit? In this paper, we generalized previous results and prove that when q is a multiple of 2 or 3 the answer is positive. We also show that when q is a prime number the answer is negative. In addition, we prove that any desired probability can be approximated well by a linear in n size circuit, with error less than q-n.