Computing with Noise - Phase Transitions in Boolean Formulas

Details Computing with Noise - Phase Transitions in Boolean Formulas Computing with Noise - Phase Transitions in Boolean Formulas

2009-08-27

arxiv.org/abs/0908.3981v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 2 figures

Scientific paper

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.

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