Semi-linearity, Parikh-boundedness and tree adjunct languages (Q799121)

A language L is called Parikh-bounded if there is a bounded language B contained in L such that for each x in L there exists y in B so that the commutative image of x is equal to that of y. \textit{M. Blattner} and \textit{M. Latteux} [Lect. Notes Comput. Sci. 115, 316-323 (1981; Zbl 0462.68057)] have proved that the class of context-free languages has the Parikh-bounded property. In the present paper the authors extend this result to the class of tree adjunct languages (a proper extension of the class of context-free languages). Tree adjunct grammars and languages were introduced by \textit{A. K. Joshi, L. S. Levy} and \textit{M. Takahashi} [J. Comput. Syst. Sci. 10, 136-163 (1975; Zbl 0326.68053)] in order to study certain linguistic questions.