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http://dx.doi.org/10.14317/jami.2019.023

ANALYSIS OF THE 90/150 CA GENERATED BY LINEAR RULE BLOCKS  

CHO, SUNG-JIN (Department of Applied Mathematics, Pukyong National University)
KIM, HAN-DOO (Department of Computer Engineering and Institute of Basic Sciences, Inje University)
CHOI, UN-SOOK (Department of Information and Communications Engineering, Tongmyong University)
KIM, JIN-GYOUNG (Department of Applied Mathematics, Pukyong National University)
KANG, SUNG-WON (Department of Applied Mathematics, Pukyong National University)
Publication Information
Journal of applied mathematics & informatics / v.37, no.1_2, 2019 , pp. 23-35 More about this Journal
Abstract
Self-reciprocal polynomials are important because it is possible to specify only half of the coefficients. The special case of the self-reciprocal polynomial, the maximum weight polynomial, is particularly important. In this paper, we analyze even cell 90/150 cellular automata with linear rule blocks of the form < $a_1,{\cdots},a_n,d_1,d_2,b_n,{\cdots},b_1$ >. Also we show that there is no 90/150 CA of the form < $U_n{\mid}R_2{\mid}U^*_n$ > or < $\bar{U_n}{\mid}R_2{\mid}\bar{U^*_n}$ > whose characteristic polynomial is $f_{2n+2}(x)=x^{2n+2}+{\cdots}+x+1$ where $R_2$ =< $d_1,d_2$ > and $U_n$ =< $0,{\cdots},0$ >, and $\bar{U_n}$ =< $1,{\cdots},1$ >.
Keywords
CA-polynomial; Self-reciprocal polynomial; Symmetric transition rule; Maximum weight polynomial; Linear rule blocks;
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Times Cited By KSCI : 2  (Citation Analysis)
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