Abstract
The following problem is shown to be decidable: Given a context-free grammar G and a string w ∈ X*, does there exist a string u ∈ L(G) such that w is obtained from u by deleting all substrings u i , that are elements of the symmetric Dyck set D *1 ?
The intersection of any two context-free languages can be obtained from only one context-free language by cancellation either with the smaller semi-Dyck set D ′*1 ⊂D *1 or with D *1 itself.
Also, the following is shown here for the first time: If the set EQ ≔ {x n¯x n¦ n ∈ N ⊂D ′*1 is used for this cancellation, then each recursively enumerable set can be obtained from linear context-free languages.
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Jantzen, M., Petersen, H. (1993). Cancellation in context-free languages: Enrichment by reduction. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_23
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