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Pointers in Recursion: Exploring the Tropics

Author Paulin Jacobé de Naurois

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Subject Classification

ACM Subject Classification
  • Software and its engineering → Recursion
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Complexity classes
Keywords
  • Implicit Complexity
  • Recursion Theory

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Abstract

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.

Cite As Get BibTex

Paulin Jacobé de Naurois. Pointers in Recursion: Exploring the Tropics. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.FSCD.2019.29

Author Details

Paulin Jacobé de Naurois
  • CNRS, Université Paris 13, Sorbonne Paris Cité, LIPN, UMR 7030, F-93430 Villetaneuse, France

Funding

  • Jacobé de Naurois, Paulin: Work partially supported by ANR project ELICA - ANR-14-CE25-0005.

Acknowledgements

I am grateful to the anonymous referees for their insightful and useful feedback.

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