Polishness of some topologies related to word or tree automata
Olivier Finkel, Olivier Carton, Dominique Lecomte
TL;DR
This paper investigates the topological properties of automata-related spaces, proving certain automata topologies are Polish, but highlighting limitations when extending these results to spaces of infinite labeled binary trees.
Contribution
It establishes the Polishness of the B"uchi and automatic topologies and demonstrates the limitations of these properties in the context of infinite labeled binary trees.
Findings
Büchi topology is Polish
Automatic topology is Polish
Büchi and Muller topologies are not Polish for infinite labeled binary trees
Abstract
We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.