In computer science, more particularly in formal language theory, a cyclic language is a set of strings that is closed with respect to repetition, root, and cyclic shift.
If A is a set of symbols, and A* is the set of all strings built from symbols in A, then a string set L ⊆ A* is called a formal language over the alphabet A.
The language L is called cyclic if where wn denotes the n-fold repetition of the string w, and vw denotes the concatenation of the strings v and w.[1]: Def.1 For example, using the alphabet A = {a, b }, the language is cyclic, but not regular.
[1]: Exm.2 However, L is context-free, since M = { an1bn1 an2bn2 ... ank bnk : ni ≥ 0 } is, and context-free languages are closed under circular shift; L is obtained as circular shift of M.
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