On the Expressibility of Stochastic Switching Circuits
- Creators
- Zhou, Hongchao
- Bruck, Jehoshua
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.
Additional Information
The authors would like to thank Dan Wilhelm for discussions and assistance.Files
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Additional details
- Eprint ID
- 26124
- Resolver ID
- CaltechPARADISE:2009.ETR093
- Created
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2009-09-21Created from EPrint's datestamp field
- Updated
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2019-11-22Created from EPrint's last_modified field
- Caltech groups
- Parallel and Distributed Systems Group