On Non-polar Token-Pass Brownian Circuits

Abstract

Brownian circuits are asynchronous circuits in which signals—represented as tokens—are able to fluctuate along wires. These fluctuations are used as a stochastic search mechanism to drive computations from a state of input to a state of output. Token-Pass circuits are a type of circuits in which wires will not merge or split. Rather, they are linear: each token remains on its wire during computation, and it will interact with other tokens only at points where they pass through circuit elements. The T-element, introduced in [Peper, Lee, Carmona, Cortadella, Morita, “Brownian Circuits: Fundamentals,” 2013], is a circuit element in which three wires pass through, and it was shown to be universal, provided the circuit it is employed in is Brownian. The Brownian circuit designs based on the T-element in the above paper have in common that they implicitly assume a bias in the direction in which tokens flow on average, even though tokens may fluctuate forward and backward during the course of a computation. This chapter proposes a new type of Brownian Token-Pass circuit, called Non-Polar Token-Pass Brownian Circuit, in which no such directional bias is assumed. Though most wires in such circuits do have directional bias, the few wires that don’t, allow for simpler circuit designs, as will be shown.