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Computing with Noise - Phase Transitions in Boolean Formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. This framework paves the way for obtaining new results on error-rates, function-depth and sensitivity, and their dependence on the gate-type and noise model used.

preprint2009arXivOpen access
Alexander MozeikaDavid SaadJack Raymond
Computational Complexitycond-mat.dis-nn
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Alexander MozeikaDavid SaadJack Raymond

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