Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2018.08.30
  • Accepted : 2018.11.02
  • Published : 2019.01.30
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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 $\bar{U_n}$ =< $1,{\cdots},1$ >.

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References

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