Stochastic Switching Circuit Synthesis

It has been proved that switching a relay circuit can lead to the realization of a random Boolean function. Such realization develops the deterministic digital logic. This development is the foundation of improved digital logic design. It also explained and enhanced the ability of manufacturing and designing densely packed digital circuits. In this paper, an attempt has been made to replace the classical switches with probabilistic switch or pswitch. The study seeks to answer the question whether similar theory can be evolved for stochastic functions. Algorithms have been used for synthesizing the circuits with required probability. The paper also presents new duality characteristic of series-parallel stochastic switching circuits. It replaces the series-parallel (sp) mode used by Shannon with a new subset called simple series-parallel (ssp). The paper also focuses on stochastic switching circuits, whereas Shannon's work dealt with deterministic switching circuits. Under deterministic switching circuits, each switch is defined by a Boolean variable. However under stochastic switching circuits, a Bernoulli random variable is used to define the probability of a pswitch being closed. The paper further creates a universal probability generator which is used to chart inputs for arbitrary probabilistic outputs. The paper also looks into the various uses for the results obtained from this experiment. The results may be very useful for analyzing and designing stochastic networks in various disciplines such as engineering and biology.