Abstract
If we encounter a function then we may ask whether it is continuous and next whether it is bijective, surjective or injective. With respect to cellular automata we have already dealt with continuity. This section is concerned with the second question. Also physicists may want to know whether the dynamical system defined by a cellular automaton is reversible. Physicists use cellular automata as simple models for microscopic processes. Hence there should be some interest to identify those cellular automata that can be reversed in time, i.e., which have a bijective global function [163].
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Notes
- 1.
The sets \(\tilde{\Gamma }^{+}\) and \(\tilde{\Gamma }^{-}\) can be interpreted as the closure and the interior of \(\tilde{\Gamma }\).
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Hadeler, KP., Müller, J. (2017). Surjectivity and Injectivity of Global Maps. In: Cellular Automata: Analysis and Applications. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-53043-7_9
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