Linear context-free tree languages and inverse homomorphisms

Linear Context-Free Tree Languages and Inverse Homomorphisms

We prove that the class of linear context-free tree languages is not closed under inverse linear tree homomorphisms. The proof is by contradiction: we encode Dyck words into a context-free tree language and prove that its preimage under a certain linear tree homomorphism cannot be generated by any context-free tree grammar. A positive result can still be obtained: the linear monadic context-fre...

Restarting Tree Automata and Linear Context-Free Tree Languages

Inverse Monoids, Trees, and Context-Free Languages

This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form ei = fi, i E I , where ei and fi are Dyck words, i.e. idempotents of the free inverse monoid on X. Some general results of Stephen are used to reduce the word problem for such a presentation to the membership problem for a certain subtree of the Cayley graph of the free group on X. In t...

Context-Free Tree languages for Descendants

The preservation of regular tree languages through rewriting, has already been studied. In this paper, we study the preservation of context-free tree languages through rewriting, for constructor-based term rewrite systems. We give positive and negative results. Positive results are effective since we give algorithms to build context-free grammars.

Non-Self-Embedding Linear Context-Free Tree Grammars Generate Regular Tree Languages

For the class of linear context-free tree grammars, we define a decidable property called self-embedding. We prove that each non-self-embedding grammar in this class generates a regular tree language and show how to construct the equivalent regular tree grammar.