The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Um autômato celular com conservação de número (NCCA) é um autômato celular tal que todos os estados das células são representados por números inteiros e o número total de sua configuração é conservado ao longo de seu processo de computação. Em contraste com os autômatos celulares normais, existem infinitas atribuições de estados para NCCAs com um número de estado constante. Quanto aos NCCAs vizinhos de von Neumann (raio um) com simetria de rotação, uma função local pode ser representada pela soma de quatro funções binárias. Neste artigo, mostramos que o tamanho mínimo do conjunto de estados do vizinho NCCA de von Neumann com rotação simétrica é 5 usando esta representação.
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Naonori TANIMOTO, Katsunobu IMAI, Chuzo IWAMOTO, Kenichi MORITA, "On the Non-existance of Rotation-Symmetric von Neumann Neighbor Number-Conserving Cellular Automata of Which the State Number is Less than Four" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 2, pp. 255-257, February 2009, doi: 10.1587/transinf.E92.D.255.
Abstract: A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. In constrast to normal cellular automata, there are infinitely many assignments of states for NCCAs with a constant state number. As for von Neumann neighbor(radius one) NCCAs with rotation-symmetry, a local function can be represented by summation of four binary functions. In this paper, we show that the minimum size of state set of rotation-symmetric von Neumann neighbor NCCA is 5 by using this representation.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.255/_p
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@ARTICLE{e92-d_2_255,
author={Naonori TANIMOTO, Katsunobu IMAI, Chuzo IWAMOTO, Kenichi MORITA, },
journal={IEICE TRANSACTIONS on Information},
title={On the Non-existance of Rotation-Symmetric von Neumann Neighbor Number-Conserving Cellular Automata of Which the State Number is Less than Four},
year={2009},
volume={E92-D},
number={2},
pages={255-257},
abstract={A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. In constrast to normal cellular automata, there are infinitely many assignments of states for NCCAs with a constant state number. As for von Neumann neighbor(radius one) NCCAs with rotation-symmetry, a local function can be represented by summation of four binary functions. In this paper, we show that the minimum size of state set of rotation-symmetric von Neumann neighbor NCCA is 5 by using this representation.},
keywords={},
doi={10.1587/transinf.E92.D.255},
ISSN={1745-1361},
month={February},}
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TY - JOUR
TI - On the Non-existance of Rotation-Symmetric von Neumann Neighbor Number-Conserving Cellular Automata of Which the State Number is Less than Four
T2 - IEICE TRANSACTIONS on Information
SP - 255
EP - 257
AU - Naonori TANIMOTO
AU - Katsunobu IMAI
AU - Chuzo IWAMOTO
AU - Kenichi MORITA
PY - 2009
DO - 10.1587/transinf.E92.D.255
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E92-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2009
AB - A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. In constrast to normal cellular automata, there are infinitely many assignments of states for NCCAs with a constant state number. As for von Neumann neighbor(radius one) NCCAs with rotation-symmetry, a local function can be represented by summation of four binary functions. In this paper, we show that the minimum size of state set of rotation-symmetric von Neumann neighbor NCCA is 5 by using this representation.
ER -