Q-VFCA: Q-state vector-valued fuzzy cellular automata

Yuki Nishida; Sennosuke Watanabe; Akiko Fukuda; Yoshihide Watanabe

Q-VFCA: Q-state vector-valued fuzzy cellular automata

Yuki Nishida, Sennosuke Watanabe, Akiko Fukuda, Yoshihide Watanabe

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

Abstract

Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.

37B15, 68Q80

Original language	English
Journal	Unknown Journal
Publication status	Published - 2020 Feb 7

Keywords

Cellular automata
Conservation law
Fuzzy cellular automata
Number-conserving rule
Periodic boundary condition
Vector-valued cellular automata

ASJC Scopus subject areas

General

Fingerprint Dive into the research topics of 'Q-VFCA: Q-state vector-valued fuzzy cellular automata'. Together they form a unique fingerprint.

Cite this

@article{766f0a01edc04eb49a59dffb37552d96,

title = "Q-VFCA: Q-state vector-valued fuzzy cellular automata",

abstract = "Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.37B15, 68Q80",

keywords = "Cellular automata, Conservation law, Fuzzy cellular automata, Number-conserving rule, Periodic boundary condition, Vector-valued cellular automata",

author = "Yuki Nishida and Sennosuke Watanabe and Akiko Fukuda and Yoshihide Watanabe",

year = "2020",

month = feb,

day = "7",

language = "English",

journal = "Unknown Journal",

}

TY - JOUR

T1 - Q-VFCA

T2 - Q-state vector-valued fuzzy cellular automata

AU - Nishida, Yuki

AU - Watanabe, Sennosuke

AU - Fukuda, Akiko

AU - Watanabe, Yoshihide

PY - 2020/2/7

Y1 - 2020/2/7

N2 - Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.37B15, 68Q80

AB - Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.37B15, 68Q80

KW - Cellular automata

KW - Conservation law

KW - Fuzzy cellular automata

KW - Number-conserving rule

KW - Periodic boundary condition

KW - Vector-valued cellular automata

UR - http://www.scopus.com/inward/record.url?scp=85093435003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85093435003&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85093435003

JO - Unknown Journal

JF - Unknown Journal

ER -