Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 1, 2009 | public
Report Open

On the Expressibility of Stochastic Switching Circuits

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

etr093.pdf
Files (283.3 kB)
Name Size Download all
md5:fd91f6c304f9f6223960f7cf4b7b4866
283.3 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 24, 2023