Some connections between nonuniform and uniform complexity classes
Richard M. Karp, Richard J. Lipton · 1980
It is well known that every set in P has small circuits [13]. Adleman [1] has recently proved the stronger result that every set accepted in polynomial time by a randomized Turing machine has small circuits. Both these results are typical of the known relationships between uniform and nonuniform complexity bounds. They obtain a nonuniform upper bound as a consequence of a uniform upper bound.