Elliptic curves over finite fields and reversibility of additive cellular automata on square grids

被引：4

作者：

Yamagishi, Masakazu ^{[1
]}

机构：

[1] Nagoya Inst Technol, Dept Math, Showa Ku, Nagoya, Aichi 4668555, Japan

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 19卷 / 01期

关键词：

sigma(+)-Automaton; Graph Laplacian; Lights Out puzzle; Elliptic curve; Chebyshev polynomial; CHEBYSHEV-POLYNOMIALS; HARMONIC-FUNCTIONS; SIGMA-AUTOMATA; LATTICES; VALUES;

D O I：

10.1016/j.ffa.2012.08.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that there are infinitely many primitive irreversible additive cellular automata on square grids for any base finite prime field by using some algebraic, in particular elliptic, curves. This gives an affirmative answer to a question of Hunziker, Machiavelo, and Park. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：105 / 119

页数：15

共 14 条

[1] [Anonymous], PURE APPL MATH
[2] [Anonymous], 2006, An introduction to the theory of numbers
[3] Mahler's measure and special values of L-functions
Boyd, DW
[J]. EXPERIMENTAL MATHEMATICS, 1998, 7 (01) : 37 - 82
[4] Cremona J. E., 1997, ALGORITHMS MODULAR E
[5] Fibonacci polynomials and parity domination in grid graphs
Goldwasser, J
Klostermeyer, W
Ware, H
[J]. GRAPHS AND COMBINATORICS, 2002, 18 (02) : 271 - 283
[6] On the Dimension of the Space of Harmonic Functions on a Discrete Torus
Goshima, Masato
Yamagishi, Masakazu
[J]. EXPERIMENTAL MATHEMATICS, 2010, 19 (04) : 421 - 429
[7] Chebyshev polynomials over finite fields and reversibility of σ-automata on square grids
Hunziker, M
Machiavelo, A
Park, H
[J]. THEORETICAL COMPUTER SCIENCE, 2004, 320 (2-3) : 465 - 483
[8] LIGOZAT G, 1975, B SOC MATH FRANCE S, V43
[9] Schur Issai., 1973, Gesammelte Abhandlungen, VIII, P422
[10] THE OMEGA-GAME AND CELLULAR AUTOMATA
SUTNER, K
[J]. AMERICAN MATHEMATICAL MONTHLY, 1990, 97 (01) : 24 - 34

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