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Adding global forbidding context to context-free grammars. (English) Zbl 0603.68078
A 1S grammar generalizes a context-free grammar in the following way: a production \(A\to \alpha\) can be applied to a string uAv (to rewrite the designated occurrence of A) provided that all letters from u belong to a fixed alphabet X and all letters from v belong to a fixed alphabet Z (the alphabets X and Z are independent of the production). It is proved that a language is generated by a 1S grammar if and only if it is context-free: this solves an open problem from the theory of selective substitution grammars [H. C. M. Kleijn and G. Rozenberg, Inf. Control 48, 221-260 (1981; Zbl 0469.68080); corrigendum ibid. 52, 364 (1982; Zbl 0506.68064)].

MSC:
68Q45 Formal languages and automata
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