Polynomial Computations in Non-Deterministic Loop-Programs and PL-Programs

It was previously shown that a slight variant of the loop-programs produces a hierarchy [formula omitted] of classes of functions defined by modified loop-programs, such that y '2is the set gal of functions computable in a polynomial number of steps by such programs. Here, an element of nondeterminism is introduced into loop-programs to produce a corresponding hierarchy [formula omitted]. Designating the set of functions polynomially computable by nondeterministic programs by [formula omitted] we prove that iff. [formula omitted] - We also prove that. [formula omitted] for n>2. Finally, an element of non-determinism is introduced in the more general PL-programs, with parallel results.