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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Cyclic language | 1/1 | https://en.wikipedia.org/wiki/Cyclic_language | reference | science, encyclopedia | 2026-05-05T11:32:26.009151+00:00 | kb-cron |
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.
== Definition == 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
∀w∈A*. ∀n>0. w ∈ L ⇔ wn ∈ L, and ∀v,w∈A*. vw ∈ L ⇔ wv ∈ L, where wn denotes the n-fold repetition of the string w, and vw denotes the concatenation of the strings v and w.
== Examples == For example, using the alphabet A = {a, b }, the language
is cyclic, but not regular. 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.
== References ==