Tree-Automatic Well-Founded Trees
Logic in Computer Science
2015-07-01 v3 Logic
Abstract
We investigate tree-automatic well-founded trees. Using Delhomme's decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. Moreover, we make a step towards proving that the ranks of tree-automatic well-founded partial orders are bounded by omega^omega^omega: we prove this bound for what we call upwards linear partial orders. As an application of our result, we show that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_{omega^omega} of the hyperarithmetical hierarchy with respect to Turing-reductions.
Keywords
Cite
@article{arxiv.1201.5495,
title = {Tree-Automatic Well-Founded Trees},
author = {Martin Huschenbett and Alexander Kartzow and Jiamou Liu and Markus Lohrey},
journal= {arXiv preprint arXiv:1201.5495},
year = {2015}
}
Comments
Will appear in Logical Methods of Computer Science