Von Neumann’s critique of automata theory and logic in computer science

In a sufficiently long chain of operations the cumulative effect of these individual probabilities of failure may (if unchecked) reach the order of magnitude of unity-at whichpoint it produces, in effect, complete unreliability. I might mention that an electromechanical relay ( a telephone relay) is at present considered acceptable if its probability of failure on an individual operation is of the order 10-s. The operations of logic (syllogisms, conjunctions, disjunctions, negations, etc., that is, in the terminology that is customary for automata, various forms of gating, coincidence, anti-coincidence, blocking, etc., actions) will all have to be treated by procedures which allow exceptions ( malfunctions ) with low but non-zero probabilities.

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