Recovering highly-complex linear recurrences of integer sequences

Gadi Aleksandrowicz; Andrei Asinowski; Gill Barequet; Ronnie Barequet

doi:10.1016/j.ipl.2017.07.006

Recovering highly-complex linear recurrences of integer sequences

Gadi Aleksandrowicz, Andrei Asinowski, Gill Barequet, Ronnie Barequet

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We suggest a variant of the Berlekamp–Massey algorithm, originally used for recovering a linear shift register from known output bits, for recovering a linear recurrence satisfied by a sequence of natural numbers from known values of the sequence. We present an application of the algorithm to recovering extremely complex recurrences satisfied by the sequences enumerating polyominoes on twisted cylinders.

Original language	English
Pages (from-to)	62-66
Number of pages	5
Journal	Information Processing Letters
Volume	127
DOIs	https://doi.org/10.1016/j.ipl.2017.07.006
State	Published - Nov 2017

Keywords

Algorithms
Chinese remainder theorem
Polyominoes
Recurrence formula

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2017.07.006

Cite this

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title = "Recovering highly-complex linear recurrences of integer sequences",

abstract = "We suggest a variant of the Berlekamp–Massey algorithm, originally used for recovering a linear shift register from known output bits, for recovering a linear recurrence satisfied by a sequence of natural numbers from known values of the sequence. We present an application of the algorithm to recovering extremely complex recurrences satisfied by the sequences enumerating polyominoes on twisted cylinders.",

keywords = "Algorithms, Chinese remainder theorem, Polyominoes, Recurrence formula",

author = "Gadi Aleksandrowicz and Andrei Asinowski and Gill Barequet and Ronnie Barequet",

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year = "2017",

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doi = "10.1016/j.ipl.2017.07.006",

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AU - Aleksandrowicz, Gadi

AU - Asinowski, Andrei

AU - Barequet, Gill

AU - Barequet, Ronnie

PY - 2017/11

Y1 - 2017/11

N2 - We suggest a variant of the Berlekamp–Massey algorithm, originally used for recovering a linear shift register from known output bits, for recovering a linear recurrence satisfied by a sequence of natural numbers from known values of the sequence. We present an application of the algorithm to recovering extremely complex recurrences satisfied by the sequences enumerating polyominoes on twisted cylinders.

AB - We suggest a variant of the Berlekamp–Massey algorithm, originally used for recovering a linear shift register from known output bits, for recovering a linear recurrence satisfied by a sequence of natural numbers from known values of the sequence. We present an application of the algorithm to recovering extremely complex recurrences satisfied by the sequences enumerating polyominoes on twisted cylinders.

KW - Algorithms

KW - Chinese remainder theorem

KW - Polyominoes

KW - Recurrence formula

UR - http://www.scopus.com/inward/record.url?scp=85025709862&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2017.07.006

DO - 10.1016/j.ipl.2017.07.006

M3 - مقالة

SN - 0020-0190

VL - 127

SP - 62

EP - 66

JO - Information Processing Letters

JF - Information Processing Letters

ER -

Recovering highly-complex linear recurrences of integer sequences

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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