License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2012.62
URN: urn:nbn:de:0030-drops-36641
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3664/
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Baillot, Patrick ; Dal Lago, Ugo

Higher-Order Interpretations and Program Complexity

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Abstract

Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some
complexity bounds on programs. This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes. In this paper, we extend this approach to the higher-order setting. For that we consider the notion of simply-typed term rewriting systems, we define higher-order polynomial interpretations for them and give a criterion ensuring that a program can be executed in polynomial time. In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination criterion based on linear types and path-like orders.

BibTeX - Entry

@InProceedings{baillot_et_al:LIPIcs:2012:3664,
  author =	{Patrick Baillot and Ugo Dal Lago},
  title =	{{Higher-Order Interpretations and Program Complexity}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{62--76},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3664},
  URN =		{urn:nbn:de:0030-drops-36641},
  doi =		{10.4230/LIPIcs.CSL.2012.62},
  annote =	{Keywords: implicit complexity, higher-order rewriting, quasi-interpretations}
}

Keywords: implicit complexity, higher-order rewriting, quasi-interpretations
Collection: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue Date: 2012
Date of publication: 03.09.2012

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