## Statistics Papers

#### Document Type

Conference Paper

#### Date of this Version

2009

#### Publication Source

Proceedings of the 2009 IEEE International Conference on Symposium on Information Theory

#### Volume

3

#### Start Page

2066

#### Last Page

2070

#### 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 ∊ 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 ∊ is bounded by a constant multiple of ∊ 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.

#### Recommended Citation

Loh, P.,
Zhou, H.,
&
Bruck, J.
(2009).
The Robustness of Stochastic Switching Networks.
*Proceedings of the 2009 IEEE International Conference on Symposium on Information Theory,*
*3*
2066-2070.
Retrieved from https://repository.upenn.edu/statistics_papers/115

**Date Posted:** 27 November 2017