English

Weak index versus Borel rank

Information Theory 2008-02-21 v1 math.IT

Abstract

We investigate weak recognizability of deterministic languages of infinite trees. We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, we propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states. The algorithm works within the time of solving the emptiness problem.

Keywords

Cite

@article{arxiv.0802.2842,
  title  = {Weak index versus Borel rank},
  author = {Filip Murlak},
  journal= {arXiv preprint arXiv:0802.2842},
  year   = {2008}
}
R2 v1 2026-06-21T10:14:10.861Z