Elsevier

Parallel Computing

Volume 23, Issue 11, 15 November 1997, Pages 1613-1634
Parallel Computing

Special paper
Linear cellular automata and Fischer automata

https://doi.org/10.1016/S0167-8191(97)00080-XGet rights and content

Abstract

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have maximal complexity. By contrast, the complexity of higher iterates of a cellular automaton always stays below the theoretical upper bound.

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