Safe Weak Minimization Revisited

Abstract

Minimization operators of different strengths have been studied in the framework of "predicative (safe) recursion." In this paper, a modification of these operators is presented. By adding the new operator to those used by Bellantoni--Cook and Leivant to characterize the polynomial-time computable functions, one obtains a characterization of the nondeterministic polynomial-time computable multifunctions. Thus the generation of the nondeterministic polytime multifunctions from the deterministic polytime functions parallels the generation of the computable functions from the primitive recursive ones.