Cancellation in context-free languages: Enrichment by reduction

Abstract

The following problem is shown to be decidable: Given a context-free grammar G and a string ω ∈ X*, does there exist a string u ∈ L(G) such that ω is obtained from u by deleting all substrings u, that are elements of the symmetric Dyck set D1*? 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 D1'* ⊂ D1* or with D1* itself. Also, the following is shown here for the first time: If the set (formula presented) is used for this cancellation, then each recursively enumerable set can be obtained from linear context-free languages.