On Omega Context Free Languages which are Borel Sets of Infinite Rank

TL;DR

This paper advances the understanding of omega context free languages by demonstrating the existence of such languages that are Borel sets of infinite rank, extending the topological classification of these languages.

Contribution

It proves the existence of omega-CFL that are Borel sets of infinite rank, answering open questions about their topological complexity.

Findings

Existence of omega-CFL with infinite Borel rank

Omega-CFL exhaust finite Borel hierarchy

Some omega-CFL are analytic but non-Borel

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].