Abstract
In this paper, we investigate some combinatorial aspects ofC-surjective local maps, i.e., local maps inducing surjective global maps,C F -surjective local maps, i.e., local maps inducing surjective restrictions of global maps on the setC F of finite configurations, andC-injective local maps, i.e., local maps inducing injective local maps, of one-dimensional tessellation automata.
We introduce a pair of right and left bundle-graphs and a pair of right and leftλ-bundle-graphs for everyC-surjective local map. We give characterizations forC F -surjectivity,C-injectivity and some other properties ofC-surjective local maps in relation to these bundle-graphs. We also establish some properties of the inverse of aC-injective local map.
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A preliminary version of a part of this paper was presented at International Symposium on Uniformly Structured Automata and Logic, Tokyo 1975 [13].
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Nasu, M. Local maps inducing surjective global maps of one-dimensional tessellation automata. Math. Systems Theory 11, 327–351 (1977). https://doi.org/10.1007/BF01768485
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DOI: https://doi.org/10.1007/BF01768485