Abstract
The k-adjacent derivations, which generate the k-adjacent languages, were introduced by Kleijn and Rozenberg as an intermediate rewriting process between context-free rewriting and EOL rewriting. In this paper, we study the generative power of the k-adjacent derivations, in continuation of the work of Gonczarowski and Shamir, and Dahlhaus and Gaifman. We show that these derivations generate languages which satisfy the following: 1. • for all k ⩾ 2, the family of the k-adjacent languages contains all EOL languages generated by expanding grammars (this is a generalization of the result of Dahlhaus and Gaifman where k = 2); 2. • for all k ⩾ 3, the family of the k-adjacent languages contains all ETOL languages generated by expanding grammars; 3. • for k > 2, ( k + l)-adjacency has the same generative power as k-adjacency if the productions right-hand sides are large enough; 4. • there are k-adjacent languages, k ⩾ 3, which are not ETOL.
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