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/
Jacobé de Naurois, Paulin
Pointers in Recursion: Exploring the Tropics
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: |
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Implicit Complexity, Recursion Theory |
Collection: |
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4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019) |
Issue Date: |
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2019 |
Date of publication: |
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18.06.2019 |