On the Expressibility of Stochastic Switching Circuits

Zhou, Hongchao and Bruck, Jehoshua (2009) On the Expressibility of Stochastic Switching Circuits. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechPARADISE:2009.ETR093]

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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 denominator q n (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 propose a greedy algorithm to realize desired reachable probabilities, and thousands of experiments show that this algorithm can achieve almost optimal size. Finally, we prove that any desired probability can be approximated well by a linear size circuit.

EPrint Type:	Monograph (Technical Report)
Additional Information:	The authors would like to thank Dan Wilhelm for discussions and assistance.
Subjects:	All Records
ID Code:	124
Deposited By:	Caltech Library System
Deposited On:	21 September 2009
Record Number:	CaltechPARADISE:2009.ETR093
Official Persistent URL:	http://resolver.caltech.edu/CaltechPARADISE:2009.ETR093
Official Citation:	Hongchao Zhou and Jehoshua Bruck. On the Expressibility of Stochastic Switching Circuits. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechPARADISE:2009.ETR093]
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