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 does. From this we can deduce regularity and context-freeness preservation properties for a generalization of tagged bifix systems.

• Type: Journal
• Year: 2011
• Where: FOSSACS
• Authors: Didier Caucal, Dinh Trong Hieu
• Keywords: FOSSACS 2011, Free Languages, Rewriting System, Software Engineering, System R