Abstract
Holonomic techniques have deep roots going back to Wallis, Euler, and Gauss, and have evolved in modern times as an important subfield of computer algebra, thanks in large part to the work of Zeilberger and others over the past three decades. In this talk, I will give an overview of the area, and in particular will present a select survey of known and original results on decision problems for holonomic sequences and functions. (Holonomic sequences satisfy linear recurrence relations with polynomial coefficients, and holonomic functions satisfy linear differential equations with polynomial coefficients.) I will also discuss some surprising connections to the theory of periods and exponential periods, which are classical objects of study in algebraic geometry and number theory; in particular, I will relate the decidability of certain decision problems for holonomic sequences to deep conjectures about periods and exponential periods, notably those due to Kontsevich and Zagier.
BibTeX - Entry
@InProceedings{ouaknine:LIPIcs:2020:13245,
author = {Jo{\"e}l Ouaknine},
title = {{Holonomic Techniques, Periods, and Decision Problems (Invited Talk)}},
booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
pages = {4:1--4:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-174-0},
ISSN = {1868-8969},
year = {2020},
volume = {182},
editor = {Nitin Saxena and Sunil Simon},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13245},
URN = {urn:nbn:de:0030-drops-132451},
doi = {10.4230/LIPIcs.FSTTCS.2020.4},
annote = {Keywords: holonomic techniques, decision problems, recurrence sequences, minimal solutions, Positivity Problem, continued fractions, special functions, periods, exponential periods}
}
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Keywords: |
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holonomic techniques, decision problems, recurrence sequences, minimal solutions, Positivity Problem, continued fractions, special functions, periods, exponential periods |
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Collection: |
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40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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04.12.2020 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)