Abstract
A string y is in C(x), the commutative image of a string x, if y is a permutation of the symbols in x. A language L is Parikh-bounded if L contains a bounded language B and all x in L have a corresponding y in B such that x is in C(y). The central result in this paper is that if L is context-free it is also Parikh-bounded. Parikh's theorem follows as a corollary. If L is not bounded but is a Parikh-bounded language closed under intersection with regular sets, then for any positive integer k there is an x in L such that #(C(x) ∩ L) ≥ k. The notion of Parikh-discreteness is introduced.
Cite
CITATION STYLE
Blattner, M., & Latteux, M. (1981). Parikh-bounded languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 115 LNCS, pp. 316–323). Springer Verlag. https://doi.org/10.1007/3-540-10843-2_26
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