The most general conservation law for a cellular automaton

被引：0

作者：

Formenti, Enrico ^{[1
]}

Kari, Jarkko ^{[2
]}

Taati, Siamak ^{[2
,3
]}

机构：

[1] Univ Nice Sophia Antipolis, Dept Informat, Parc Valrose, F-06108 Nice 2, France

[2] Univ Turku, Dept Math, FI-20014 Turku, Finland

[3] Turku Ctr Comp Sci, FI-20520 Turku, Finland

来源：

COMPUTER SCIENCE - THEORY AND APPLICATIONS | 2008年 / 5010卷

基金：

芬兰科学院;

关键词：

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-valued) conservation law, encapsulating all conservation laws of that range. For one-dimensional CA the semigroup corresponding to such a most general conservation law has an effectively constructible finite presentation, while for higher-dimensional ones no such effective construction exists.

引用

页码：194 / +

页数：2

共 50 条

[21] A SOLITON CELLULAR AUTOMATON
TAKAHASHI, D
SATSUMA, J
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1990, 59 (10) : 3514 - 3519
[22] CELLULAR AUTOMATON CRYPTOSYSTEMS
Rososhek, S. K.
Borovkov, A. A.
Evsutin, O. O.
PRIKLADNAYA DISKRETNAYA MATEMATIKA, 2008, 1 (01): : 43 - 49
[23] A Morphogenetic Cellular Automaton
Beros, Achilles
Chyba, Monique
Fronville, Alexandra
Mercier, Frederic
2018 ANNUAL AMERICAN CONTROL CONFERENCE (ACC), 2018, : 1987 - 1992
[24] CELLULAR AUTOMATON SUPERCOLLIDERS
Martinez, Genaro J.
Adamatzky, Andrew
Stephens, Christopher R.
Hoeflich, Alejandro F.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2011, 22 (04): : 419 - 439
[25] A chaos cellular automaton
Nakagawa, M
STATISTICAL PHYSICS, 2000, 519 : 232 - 234
[26] LAW OF CORRESPONDING STATES IN ITS MOST GENERAL FORM
HAKALA, RW
JOURNAL OF PHYSICAL CHEMISTRY, 1967, 71 (06): : 1880 - &
[27] GENERAL COVARIANT ENERGY-MOMENTUM CONSERVATION LAW IN GENERAL SPACETIME
DUAN, YS
LIU, JC
DONG, XG
GENERAL RELATIVITY AND GRAVITATION, 1988, 20 (05) : 485 - 496
[28] A cellular automaton model of cellular signal transduction
Wurthner, JU
Mukhopadhyay, AK
Peimann, CJ
COMPUTERS IN BIOLOGY AND MEDICINE, 2000, 30 (01) : 1 - 21
[29] A general workload conservation law with applications to queueing systems
El-Taha, Muhammad
QUEUEING SYSTEMS, 2017, 85 (3-4) : 361 - 381
[30] A conservation law formulation of nonlinear elasticity in general relativity
Gundlach, Carsten
Hawke, Ian
Erickson, Stephanie J.
CLASSICAL AND QUANTUM GRAVITY, 2012, 29 (01)

← 1 2 3 4 5 →