A quantifier characterization for nondeterministic log space

It is well known [C] that nondeterministic polynomial time computabilit y may be characterized in terms of deterministic polynomial time computabilit y as follows : A set A is in NP iff there exist a polynomial p and a deterministic polynomial time computable predicate R such tha t x A <--> (Ry )[I y l 5 P(Ixl ) (Vertical bars refer to the length of the enclosed string . ) This characterization provides a clean way to understand nondeterministi c time . It also provides a basis for the alternating quantifier hierarch y studied in [St], [SM] and [W] .