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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.

- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.2 pp.255-257

- Publication Date
- 2009/02/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E92.D.255

- Type of Manuscript
- Special Section LETTER (Special Section on Foundations of Computer Science)

- Category

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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 -