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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Hongchao Zhou Ho-Lin Chen Bruck, J. |
| Copyright Year | 2010 |
| Description | Author affiliation: Department of Electrical Engineering, California Institute of Technology, Pasadena, 91125, USA (Hongchao Zhou; Bruck, J.) || Center for Mathematics of Information, California Institute of Technology, Pasadena, 91125, USA (Ho-Lin Chen) |
| Abstract | A stochastic flow network is a directed graph with incoming edges (inputs) and outgoing edges (outputs), tokens enter through the input edges, travel stochastically in the network and can exit the network through the output edges. Each node in the network is a splitter, namely, a token can enter a node through an incoming edge and exit on one of the output edges according to a predefined probability distribution. We address the following synthesis question: Given a finite set of possible splitters and an arbitrary rational probability distribution, design a stochastic flow network, such that every token that enters the input edge will exit the outputs with the prescribed probability distribution. The problem of probability synthesis dates back to von Neummann's 1951 work and was followed, among others, by Knuth and Yao in 1976, who demonstrated that arbitrary rational probabilities can be generated with tree networks; where minimizing the expected path length, the expected number of coin tosses in their paradigm, is the key consideration. Motivated by the synthesis of stochastic DNA based molecular systems, we focus on designing optimal-sized stochastic flow networks (the size of a network is the number of splitters). We assume that each splitter has two outgoing edges and is unbiased (probability per output edge). We show that an arbitrary rational probability aoverb with a ≤ b ≤ $2^{n}$ can be realized by a stochastic flow network of size n, we also show that this is optimal. We note that our stochastic flow networks have feedback (cycles in the network), in fact, we demonstrate that feedback improves the expressibility of stochastic flow networks, since without feedback only probabilities of the form $aover2^{n}$ (a an integer) can be realized. |
| Starting Page | 1330 |
| Ending Page | 1334 |
| File Size | 178197 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424478903 |
| e-ISBN | 9781424478927 |
| e-ISBN | 9781424478910 |
| DOI | 10.1109/ISIT.2010.5513754 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-06-13 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Network synthesis Stochastic processes Probability distribution Stochastic systems DNA Feedback Tree graphs Tail Computer networks Control system synthesis |
| Content Type | Text |
| Resource Type | Article |
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