On Omega Context Free Languages which are Borel Sets of Infinite Rank
Abstract
This paper is a continuation of the study of topological properties of omega context free languages (omega-CFL). We proved before that the class of omega-CFL exhausts the hierarchy of Borel sets of finite rank, and that there exist some omega-CFL which are analytic but non Borel sets. We prove here that there exist some omega context free languages which are Borel sets of infinite (but not finite) rank, giving additional answer to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621].
Cite
@article{arxiv.1005.5633,
title = {On Omega Context Free Languages which are Borel Sets of Infinite Rank},
author = {Olivier Finkel},
journal= {arXiv preprint arXiv:1005.5633},
year = {2010}
}
Comments
The supremum of the set of Borel ranks of omega-context-free languages is actually greater than the first non-recursive ordinal. This has been proved later in a paper "Borel Ranks and Wadge Degrees of Omega Context Free Languages" published in the journal Mathematical Structures in Computer Science (2006)