title: Noisy random Boolean formulae: a statistical physics perspective.
abstract: Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.
authors.affiliation: The Non-linearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom. a.s.mozeika@aston.ac.uk
authors.forename: Alexander
authors.initials: A
authors.lastname: Mozeika
authors.forename: David
authors.initials: D
authors.lastname: Saad
authors.forename: Jack
authors.initials: J
authors.lastname: Raymond
mesh_terms: D008128:Logic; D008962:Models, Theoretical; D055585:Physical Phenomena; D015203:Reproducibility of Results; D013269:Stochastic Processes