Algebraic characterization of logically defined tree languages
Logic in Computer Science
2010-06-21 v3 Logic
Abstract
We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindstr\"om quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. Our results generalize analogous results on finite word languages, but it must be noted that, as they stand, they do not yield an algorithm to decide whether a given regular tree language is first-order definable.
Cite
@article{arxiv.0709.2962,
title = {Algebraic characterization of logically defined tree languages},
author = {Zoltan Esik and Pascal Weil},
journal= {arXiv preprint arXiv:0709.2962},
year = {2010}
}
Comments
46 pages. Version 3: various local improvements (more typos corrected, and "intuitive" explanations added)