한국전자통신학회논문지 (The Journal of the Korea institute of electronic communication sciences)

한국전자통신학회 (Korea Institute of Electronic Communication Science)
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Uniform CA와 90/150 Hybrid CA의 합성

Synthesis of Uniform CA and 90/150 Hybrid CA

  • 투고 : 2016.02.24
  • 심사 : 2016.03.24
  • 발행 : 2016.03.31
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초록

본 논문에서는 전이규칙이 모두 102인 Uniform CA(Uniform Cellular Automata, UCA) $\mathbb{C}_u$와 특성다항식이 $(x+1)^m$인 m-셀 90/150 hybrid CA $\mathbb{C}_h$를 합성한 CA의 특성을 분석한다. 먼저 $\mathbb{C}_u$로부터 유도된 여원 그룹 CA의 사이클 구조를 분석하고 이를 통해 모든 사이클의 길이가 같아지는 여원 CA의 조건을 제시한다. 그리고 $\mathbb{C}_u$와 $\mathbb{C}_h$를 합성한 CA $\mathbb{C}$의 최소다항식이 $(x+1)^q$일 때 $(T+I)^{q-1}F{\neq}0$을 만족하는 F를 여원벡터로 택하여 구성한 여원 그룹 CA $\mathbb{C}^{\prime}$의 사이클 구조를 분석한다.

In this paper we analyze the CA formed by combining the uniform 102 CA $\mathbb{C}_u$ and the m-cell 90/150 hybrid CA $\mathbb{C}_h$ whose characteristic polynomial is $(x+1)^m$. We analyze cycle structures of complemented group CA derived from $\mathbb{C}_u$ and propose a condition of complemented CA dividing the entire state space into smaller cycles of equal lengths. And we analyze the cycle structure of complemented group CA $\mathbb{C}^{\prime}$ derived from the CA $\mathbb{C}$ formed by combining $\mathbb{C}_u$ and $\mathbb{C}_h$ with complement vector F such that $(T+I)^{q-1}F{\neq}0$ where $(x+1)^q$ is the minimal polynomial of $\mathbb{C}$.

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참고문헌

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