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# The Synthesis and Analysis of Stochastic Switching Circuits

Zhou, Hongchao and Loh, Po-Ling and Bruck, Jehoshua (2012) The Synthesis and Analysis of Stochastic Switching Circuits. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20160203-092316194

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## Abstract

Stochastic switching circuits are relay circuits that consist of stochastic switches called pswitches. The study of stochastic switching circuits has widespread applications in many fields of computer science, neuroscience, and biochemistry. In this paper, we discuss several properties of stochastic switching circuits, including robustness, expressibility, and probability approximation. First, we study the robustness, namely, the effect caused by introducing an error of size Є to each pswitch in a stochastic circuit. We analyze two constructions and prove that simple series-parallel circuits are robust to small error perturbations, while general series-parallel circuits are not. Specifically, the total error introduced by perturbations of size less than Є is bounded by a constant multiple of Є in a simple series-parallel circuit, independent of the size of the circuit. Next, we study the expressibility of stochastic switching circuits: Given an integer q and a pswitch set S = {1/q,2/q,...,q-1/q}, can we synthesize any rational probability with denominator q^n (for arbitrary n) with a simple series-parallel stochastic switching circuit? We generalize previous results and prove that when q is a multiple of 2 or 3, the answer is yes. We also show that when q is a prime number larger than 3, the answer is no. Probability approximation is studied for a general case of an arbitrary pswitch set S = {s_1, s_2,... , s_(|S|)}. In this case, we propose an algorithm based on local optimization to approximate any desired probability. The analysis reveals that the approximation error of a switching circuit decreases exponentially with an increasing circuit size.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1209.0715arXivDiscussion Paper
ORCID:
AuthorORCID
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:Submitted on 4 Sep 2012. This work was supported in part by the NSF Expeditions in Computing Program under grant CCF-0832824. This paper was presented in part at IEEE International Symposium on Information Theory (ISIT), Seoul, Korea, June 2009.
Funders:
Funding AgencyGrant Number
NSFCCF-0832824
Subject Keywords:Stochastic Switching Circuits, Robustness, Probability Synthesis, Probability Approximation
Record Number:CaltechAUTHORS:20160203-092316194
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160203-092316194
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64187
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:03 Feb 2016 20:14