 
Summary: 1
On the Maximum Tolerable Noise of kinput Gates for
Reliable Computation by Formulas
William S. Evans Member, IEEE and Leonard J. Schulman
Abstract We determine the precise threshold of component noise
below which formulas composed of odd degree components can reliably
compute all Boolean functions.
Index Terms Computation by unreliable components, reliable com
puting
I. INTRODUCTION
We consider a model of computation that was first proposed by von
Neumann in 1952 [1]: the noisy circuit. A noisy circuit is composed
of #noisy gates. An #noisy, kinput gate is designed to compute a
Boolean function of its k Boolean inputs; however, it has the property
that for any assignment to the inputs, there is probability # that the
output of the gate is the complement of the designed value. In a noisy
circuit this event occurs independently at every gate of the circuit.
A circuit takes n Boolean values as input and produces one
Boolean output. The inputs to a gate in the circuit may be the outputs
of other gates in the circuit, inputs to the circuit, or the constants 0
