ComputingComputer ScienceMathematicsDiscrete MathematicsInformation TheoryTheory Of ComputationBoolean AlgebraBoolean Network ModelsBoolean OperationsCircuit ComplexityComputational ComplexityDigital Logic DesignBoolean Circuit ComplexityBoolean Function ComplexityBoolean FunctionsCircuit Complexity Of Boolean FunctionsCircuit Lower BoundsComplexity Of Boolean Functions
We show that many Boolean functions (including, in a certain sense, "almost all" Boolean functions) have the property that the number of noisy gates needed to compute them differs from the number of noiseless gates by at most a constant factor. This may be contrasted with results of von Neumann, Dobrushin and Ortyukov to the effect that (1) for every Boolean function, the number of noisy gates needed is larger by at most a logarithmic factor, and (2) for some Boolean functions, it is larger by at least a logarithmic factor.
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Low-density parity-check codes
Robert G. Gallager · IEEE Transactions on Information Theory · 1962 · 10.6K citations · Full text
COMBINATORICA · 1986 · 1.2K citations