The topological entropy of invertible cellular automata
The topological entropy of invertible cellular automata
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DOI：
10.1016/j.cam.2007.01.020
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发表时间：
2008-03
影响因子：
2.4
通讯作者：
H. Akın
中科院分区：
文献类型：
--
作者：
H. Akın
本文研究可逆一维线性元胞自动机的拓扑熵，利用D 'amica等定义的算法，在环Zm（m ∈ 2）上，对由Tf[-r，r]（x）=（yn）n=-∞∞，yn=f（xn-r，...，xn+r）=∑i=-rrλixn+i（modm），x=（xn）n=-∞∞∈ ZmZ和f：Zm 2 r +1→Zm给出的映射Tf[-r，r]：ZmZ→ ZmZ，[On computing the entropy of cellular automa，Theoret. Comput. Sci. 290（2003）1629-1646]。证明了如果一个一维线性元胞自动机是可逆的，那么这个元胞自动机和它的逆元胞自动机的拓扑熵是相等的。
This paper is concerned with the topological entropy of invertible one-dimensional linear cellular automata, i.e., the maps Tf[-r,r]:ZmZ→ZmZwhich are given by Tf[-r,r](x)=(yn)n=-∞∞, yn=f(xn-r,…,xn+r)=∑i=-rrλixn+i(modm), x=(xn)n=-∞∞∈ZmZand f:Zm2r+1→Zm, over the ring Zm(m⩾2) by means of algorithm defined by D’amica et al. [On computing the entropy of cellular automa, Theoret. Comput. Sci. 290 (2003) 1629–1646]. We prove that if a one-dimensional linear cellular automata is invertible, then the topological entropies of this cellular automata and its inverse are equal.