Noise abatement is the key problem of small-scaled circuit design. New computational paradigms are needed, as these circuits shrink, they become very vulnerable to noise and soft errors. In this lecture, we present a probabilistic computation framework for improving the resiliency of logic gates and circuits under random conditions induced by voltage or current fluctuation. Among many probabilistic techniques for modeling such devices, only a few models satisfy the requirements of efficient hardware implementation; specifically, Boltzman machines and Markov Random Field (MRF) models. These models have similar built-in noise immunity characteristics based on feedback mechanisms. In probabilistic models, the values 0 and 1 of logic functions are replaced by degrees of beliefs that these values occur. An appropriate metric for degree of belief is probability. We discuss various approaches for noise-resilient logic gate design, and propose a novel design taxonomy based on implementation...

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