Abstract

Introduction Every linear cellular automaton ae can be associated with a regular language L(ae) of finite words: L(ae) is the collection of all finite subwords of configurations that arise after one application of the global map of the cellular automaton. Discussions of the language theoretic aspects of linear cellular automata and sofic systems, in particular with respect to their relation to the topology of the space of configurations, can be found in [8], [10] and [7]. In this paper, we will study two measures of complexity associated with L(ae) that are based on minimal finite state machines of a certain type. The first is simply the size of the minimal automaton for L(ae), or, equivalently, the number of left quotients of this language. For the second measure, one can exploit the fact that the languages L(ae) are no

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