Lower Bounds for the Complexity of Reliable Boolean Circuits with Noisy Gates

We prove that the reliable computation of any Boolean function with sensitivity s requires Ω(s log s) gates if the gates of the circuit fail independently with a fixed positive probability. This theorem was stated by Dobrushin and Ortyukov in 1977, but their proof was found by Pippenger, Stamoulis and Tsitsiklis to contain some errors. We save the original structure of the proof of Dobrushin and Ortyukov, correcting two points in the probabilistic argument.

• Type: Conference
• Year: 1991
• Where: FOCS
• Authors: Anna Gál
• Keywords: Boolean Function, Circuit Fail, FOCS 1991, Reliable Computation, Theoretical Computer Science