Digital yet Deliberately Random: Synthesizing Logical Computation on Stochastic Bit Streams A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY

Most digital circuits process information that is encoded as zeros and ones determin-istically. For example, the arithmetic unit of a modern computer performs calculationson deterministic integer or floating-point values represented in binary radix. However,digital computation need not be deterministic. In this dissertation, we consider an al-ternative paradigm: digital circuits that compute on stochastic sequences of zeros andones. Such circuits can implement complex arithmetic operations with very simple hard-ware. For instance, multiplication can be performed with a single AND gate. Also theyare highly tolerant of soft errors (i.e., bit flips). In the first part of the dissertation, wepresent a general method for synthesizing digital circuitry that computes on stochasticbit streams. Our method can be used to synthesize arbitrary polynomial functions.Through polynomial approximations, it can also be used to synthesize non-polynomialfunctions. Experiments on polynomial functions and functions used in image process-ing show that our method produces circuits that are highly tolerant of soft errors. Theaccuracy degrades gracefully with the error rate. For applications that mandate simplehardware, producing relatively low precision computation very reliably, our method isa winning proposition.A premise for the stochastic paradigm is the availability of stochastic bit streamswith the requisite probabilities. Physical random sources can be exploited to generatesuch random bit streams. Generally, each source has a fixed bias and so provides bitsthat have a specific probability of being one versus zero. If many different probabilityvalues are required, it can be difficult or expensive to generate all of these directly fromphysical sources. In the second part of the dissertation, we demonstrate novel techniquesfor synthesizing combinational logic that transforms a set of source probabilities intodifferent target probabilities. We consider three scenarios in terms of whether the source