  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.
