The Robustness of Stochastic Switching Networks

Loh, Po-Ling and Zhou, Hongchao and Bruck, Jehoshua (2009) The Robustness of Stochastic Switching Networks. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechPARADISE:2009.ETR092]

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Abstract

Many natural systems, including chemical and biological systems, can be modeled using stochastic switching circuits. These circuits consist of stochastic switches, called pswitches, which operate with a fixed probability of being open or closed. We study the effect caused by introducing an error of size ε to each pswitch in a stochastic circuit. We analyze two constructions -— simple series-parallel and general series-parallel circuits -— 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 ε is bounded by a constant multiple of ε in a simple series-parallel circuit, independent of the size of the circuit. However, the same result does not hold in the case of more general series-parallel circuits. In the case of a general stochastic circuit, we prove that the overall error probability is bounded by a linear function of the number of pswitches.

EPrint Type:	Monograph (Technical Report)
Additional Information:	This work was supported in part by the NSF Expeditions in Computing Program under grant CCF-0832824. The authors would also like to thank the Caltech Summer Undergraduate Research Fellowship (SURF) program for its support in funding this research, and Dan Wilhelm for his comments and suggestions in revising the paper.
Subjects:	All Records
ID Code:	123
Deposited By:	Caltech Library System
Deposited On:	21 September 2009
Record Number:	CaltechPARADISE:2009.ETR092
Official Persistent URL:	http://resolver.caltech.edu/CaltechPARADISE:2009.ETR092
Official Citation:	Po-Ling Loh, Hongchao Zhou, and Jehoshua Bruck. The Robustness of Stochastic Switching Networks. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechPARADISE:2009.ETR092]
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