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Type-based analysis of logarithmic amortised complexity

Published online by Cambridge University Press:  19 October 2021

Martin Hofmann ,
Lorenz Leutgeb Open the ORCID record for Lorenz Leutgeb [Opens in a new window] ,
David Obwaller ,
Georg Moser  and
Florian Zuleger Open the ORCID record for Florian Zuleger [Opens in a new window]
Martin Hofmann
Affiliation:
Institut für Informatik, Ludwig-Maximilians-Universität München, Germany
Lorenz Leutgeb
Affiliation:
Institut für Logic and Computation 192/4, Technische Universität Wien, Austria
David Obwaller
Affiliation:
Institut für Informatik, Universität Innsbruck, Austria
Georg Moser
Affiliation:
Institut für Informatik, Universität Innsbruck, Austria
Florian Zuleger*
Affiliation:
Institut für Logic and Computation 192/4, Technische Universität Wien, Austria
*
*Corresponding author. Email: florian.zuleger@tuwien.ac.at
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Abstract

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We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist’s method of amortised analysis and is potentialbased. The type system makes use of logarithmic potential functions and is the first such system to exhibit logarithmic amortised complexity. With our approach, we target the automated analysis of self-adjusting data structures, like splay trees, which so far have only manually been analysed in the literature. In particular, we have implemented a semi-automated prototype, which successfully analyses the zig-zig case of splaying, once the type annotations are fixed.

Keywords

Analysis of algorithmsamortised resource analysisfunctional programmingself-adjusting data structuresautomation
Type
Special Issue: In Homage to Martin Hofmann
Information
Mathematical Structures in Computer Science , Volume 32 , Special Issue 6: In Homage to Martin Hofmann , June 2022 , pp. 794 - 826
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Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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