Linear Context-Free Tree Languages and Inverse Homomorphisms
Formal Languages and Automata Theory
2015-10-20 v2
Abstract
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-free tree languages are closed under inverse linear tree homomorphisms.
Cite
@article{arxiv.1510.04881,
title = {Linear Context-Free Tree Languages and Inverse Homomorphisms},
author = {Johannes Osterholzer and Toni Dietze and Luisa Herrmann},
journal= {arXiv preprint arXiv:1510.04881},
year = {2015}
}
Comments
30 pages, 1 figure; fixed a variable collision (t') in Section 7