Pointers in Recursion: Exploring the Tropics

Paulin Jacobé de Naurois
(CNRS/université paris13)

We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tiering is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras.

In Thomas Seiller and Steffen Jost: Proceedings Third Joint Workshop on Developments in Implicit Computational complExity and Foundational & Practical Aspects of Resource Analysis (DICE-FOPARA 2019), Prague, Czech Republic, 6.4.2019 - 7.4.2019, Electronic Proceedings in Theoretical Computer Science 298, pp. 31–45.
Published: 14th August 2019.

ArXived at: https://dx.doi.org/10.4204/EPTCS.298.3 bibtex PDF
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