  Typical properties of computing circuits composed of noisy logical gates are
studied using the statistical physics methodology. A growth model that gives
rise to typical random Boolean functions is mapped onto a layered Ising spin
system, which facilitates the study of their ability to represent arbitrary
formulae with a given level of error, the tolerable level of gate-noise, and
its dependence on the formulae depth and complexity, the gates used and
properties of the function inputs. Bounds on their performance, derived in the
information theory literature via specific gates, are straightforwardly
retrieved, generalized and identified as the corresponding typical-case phase
transitions. The framework is employed for deriving results on error-rates,
function-depth and sensitivity, and their dependence on the gate-type and noise
model used that are difficult to obtain via the traditional methods used in
this field.
