Regularity and Context-Freeness over Word Rewriting Systems

Didier Caucal (1) , Trong Hiêu Dinh (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domains: Logic in Computer Science [cs.LO]

Didier Caucal, Trong Hiêu Dinh. Regularity and Context-Freeness over Word Rewriting Systems. FOSSACS 2011, Mar 2011, Saarbrücken, Germany. pp.214-228, ⟨10.1007/978-3-642-19805-2_15⟩. ⟨hal-00867572⟩