Reliability of nonbranching programs in an arbitrary complete finite basis
M. A. Alekhina, S. M. Grabovskaya · Russian Mathematics · 2012
We consider the realization of Boolean functions by nonbranching programs with conditional stop operators in an arbitrary complete finite basis. We assume that conditional stop operators are absolutely reliable, while all functional operators are prone to output inverse failures independently of each other with probability ɛ in the interval (0, 1/2). We prove that any Boolean function is realizable by a program with unreliability ɛ + 81ɛ 2 for all ɛ ∈ (0, 1/960].