Safe Weak Minimization Revisited

Minimization operators of different strength 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.