2012/09/04 by Hongchao Zhou, Po‐Ling Loh, Zhou, Hongchao +4 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced biosensing and bioanalysis techniques #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1209.0715
2 columns, 15 pages
arxiv created 2012/09/04 · openalex publication_date 2012/09/04 · arxiv updated 2012/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 εto 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 εis bounded by a constant multiple of εin 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 qn (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=\s1,s2,...,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.