Regularity and Context-Freeness over Word Rewriting Systems
We describe a general decomposition mechanism to express the derivation relation of a word rewriting system R as the composition of a (regular) substitution followed by the derivation relation of a system R′ ∪ D, where R′ is a strict sub-system of R and D is the Dyck rewriting system. From this decomposition, we deduce that the system R (resp. R − 1) preserves regular (resp. context-free) languages whenever R′ ∪ D (resp. its inverse) does. From this we can deduce regularity and context-freeness preservation properties for a generalization of tagged bifix systems.
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