## Ranking primitive recursions: The low grzegorczyk classes revisited (1998)

Venue: | SIAM Journal of Computing |

Citations: | 11 - 1 self |

### BibTeX

@ARTICLE{Bellantoni98rankingprimitive,

author = {Stephen J. Bellantoni and Karl-heinz Niggl},

title = {Ranking primitive recursions: The low grzegorczyk classes revisited},

journal = {SIAM Journal of Computing},

year = {1998},

volume = {29},

pages = {401--415}

}

### OpenURL

### Abstract

Abstract. Traditional results in subrecursion theory are integrated with the recent work in “predicative recursion ” by defining a simple ranking ρ of all primitive recursive functions. The hierarchy defined by this ranking coincides with the Grzegorczyk hierarchy at and above the linearspace level. Thus, the result is like an extension of the Schwichtenberg/Müller theorems. When primitive recursion is replaced by recursion on notation, the same series of classes is obtained except with the polynomial time computable functions at the first level.

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Citation Context ...is thesis [3], p. 49, at the suggestion of S. Cook; and related linear-space results were proved independently by Handley [9] and Leivant [11]. The characterization was adapted and reproved by Nguyen =-=[18]-=- in her work on linear space reasoning. The current characterizations of E r+1 can also be compared to Leivant’s characterization of Grzegorczyk classes using “coerced recurrence”, [12] §4. Coerced re... |

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