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On the Maximum Tolerable Noise of kinput Gates for Reliable Computation by Formulas

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
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


Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology


Collections: Computer Technologies and Information Sciences