Multisymbol Majority Vote and Hard Core

This paper describes a weak sense majority-vote technique for a k symbol function g(z) as follows. If a probabilistic polynomial time algorithm A exists such that Pr[A(z) = g(z)] 1=k + , then s 4 = 2 k 1 1 probabilistic polynomial time algorithms f ^ A 1 ; : : : ; ^ A s g exist such that for 8z 2 f0; : : : ; k 1g , there exists ^ A i 2 f ^ A 1 ; : : : ; ^ A s g such that Pr[ ^ A i (z) = g(z)] 1 jzj c , where c is a constant. We apply our technique to obtain a hard core of k symbol one way funcitons.