parikh_image (744B)
1 # Parikh image 2 3 The *Parikh image* of a [word] is the [vector] of the number of occurrences of the letters that it contains, and the *Parikh image* of a [formal_language] is the set of Parikh images of the [words] that it contains 4 5 [Parikhs_theorem]: the Parikh images of [CFLs] and of [regular_languages] are the same! 6 7 The Parikh image is not always [recognizable] even for a [regular_language] 8 - https://cstheory.stackexchange.com/questions/46670/languages-whose-parikh-image-is-recognizable 9 - it relates to [regular_languages] whose [commutative_closure] is also a [regular_language] 10 - cf [commutative_closure_does_not_preserve_regularity] 11 12 Up: [formal_language_theory] 13 14 See also: [language_commutative], [length] 15 16 Aliases: parikh images