ALMOST-EVERYWHERE COMPLEXITY, BI-IMMUNITY AND NONDETERMINISTIC SPACE

We show that the complexity-theoretic notion of almost-everywhere complex functions is identical to the recursion-theoretic notion of bi-immune sets in the nondeterministic space domain. Furthermore we derive a very strong separation theorem for nondeterministic space - witnessing this fact by almost-everywhere complex sets - that is equivalent to the traditional infinitely-often complex hierarchy result. The almost-everywhere complex sets constructed here are the first such sets constructed for nondeterministic complexity classes.