Non-uniform finite Maximal length CAcellular automata (CAs) with open boundary share a special property called maximality in cycle length. It means that all but one configuration of the cellular automaton (CA) form a single cycle. In case of an n-cell binary CA, the maximal cycle length is \(2^{n}-1\) . Such a CA is traditionally referred to as the maximal length CA. Almost all the works on maximal length CAs revolve around the binary CAs with ECA rules. This chapter also primarily considers non-uniform ECAs. However, it reports some properties for non-binary cases (Sect. 6.7). The maximal length CAs are categorised as linear, complemented and non-linear.

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Maximal Length Cellular Automata

  • Sukanta Das,
  • Biplab K. Sikdar

摘要

Non-uniform finite Maximal length CAcellular automata (CAs) with open boundary share a special property called maximality in cycle length. It means that all but one configuration of the cellular automaton (CA) form a single cycle. In case of an n-cell binary CA, the maximal cycle length is \(2^{n}-1\) . Such a CA is traditionally referred to as the maximal length CA. Almost all the works on maximal length CAs revolve around the binary CAs with ECA rules. This chapter also primarily considers non-uniform ECAs. However, it reports some properties for non-binary cases (Sect. 6.7). The maximal length CAs are categorised as linear, complemented and non-linear.