License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2019.29
URN: urn:nbn:de:0030-drops-105360
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10536/
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Jacobé de Naurois, Paulin

Pointers in Recursion: Exploring the Tropics

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LIPIcs-FSCD-2019-29.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{jacobdenaurois:LIPIcs:2019:10536,
  author =	{Paulin Jacob{\'e} de Naurois},
  title =	{{Pointers in Recursion: Exploring the Tropics}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Herman Geuvers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10536},
  URN =		{urn:nbn:de:0030-drops-105360},
  doi =		{10.4230/LIPIcs.FSCD.2019.29},
  annote =	{Keywords: Implicit Complexity, Recursion Theory}
}

Keywords: Implicit Complexity, Recursion Theory
Collection: 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)
Issue Date: 2019
Date of publication: 18.06.2019

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