A Survey of Classes of Primitive Recursive Functions

摘要

This paper is a transcription of mimeographed course notes titled ``A Survey of Classes of Primitive Recursive Functions", by S.A. Cook, for the University of California Berkeley course Math 290, Sect. 14, January 1967. The notes present a survey of subrecursive function classes (and classes of relations based on these classes,) including Cobham's class L of polynomial time functions, and Bennett's class (denoted here by L + ) of extended positive rudimentary functions. It is noted that L + corresponds to those functions computable in nondeterministic polynomial time and that L L + , and it is conjectured that this inclusion is proper. Relational versions of these classes are also introduced, and a similar inclusion is noted. This is likely the earliest consideration in print of the relationship between the complexity classes P and NP, in both functional and relational forms.The numbering of sections and theorems corresponds to that in the original notes. However, page numbering does not correspond to the page numbering of the original. Minor typographical errors have been corrected.