Regularity and context-freeness over word rewriting systems

Authors:
Didier Caucal;Trong Hieu Dinh
Affiliations:
LIGM, UMR CNRS 8049, Université Paris-Est, France;LIGM, UMR CNRS 8049, Université Paris-Est, France
Venue:
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Year:
2011

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Abstract

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.