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As Si CMOS devices are scaled down into the nanoscale regime, current computer architecture approaches are reaching their practical limits. Future nano-architectures will confront devices and interconnections with a large number of inherent defects, which motivates the search for new architectural paradigms. In this paper, we examine probabilistic-based design methodologies for nanoscale computer architectures based onMarkov random fields (MRF). The MRF approach can express arbitrary logic circuits and the logic operation is achieved by maximizing the probability of correct state configurations in the logic network depending on the interaction of neighboring circuit nodes. The computation proceeds via probabilistic propagation of states through the circuit. Crucially, the MRF logic can be implemented in modified CMOS-based circuitry that trades off circuit area and operation speed for the crucial fault tolerance and noise immunity. This paper builds on the recent demonstration that significant immunity to faulty individual devices or dynamically occurring signal errors can be achieved by the propagation of state probabilities over an MRF network. In particular, we are interested in CMOS-based circuits that work reliably at very low supply voltages (VDD=0.1-0.2 V), where standard CMOS would fail due to thermal and crosstalk noise, and transistor threshold variation. In this paper, we present results for simulated probabilistic test circuits for elementary logic components and well as small circuits taken from the MCNC91 benchmark suite and we show greatly improved noise immunity operating at very low VDD. The MRF framework extends to all levels of a design, where formally optimum probabilistic computation can be implemented as a natural element of the processing structure.