In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words that represent the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms. The most widely studied shift spaces are the subshifts of finite type and the sofic shifts.
In the classical framework[1] a shift space is any subset of , where is a finite set, which is closed for the Tychonov topology and invariant by translations. More generally one can define a shift space as the closed and translation-invariant subsets of , where is any non-empty set and is any monoid.[2][3]
^Lind, Douglas A.; Marcus, Brian (1995). An introduction to symbolic dynamics and coding. Cambridge: Cambridge University press. ISBN 978-0-521-55900-3.
^Ceccherini-Silberstein, T.; Coornaert, M. (2010). Cellular automata and groups Springer Monographs in Mathematics. Springer Monographs in Mathematics. Springer Verlag. doi:10.1007/978-3-642-14034-1. ISBN 978-3-642-14033-4.
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