MSO 0-1 law for recursive random trees

We prove the monadic second-order 0-1 law for two recursive tree models: uniform attachment tree and preferential attachment tree. We also show that the first order 0-1 law does not hold for non-tree uniform attachment models.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Statistics & probability letters 2021-06, Vol.173, p.109061, Article 109061
Hauptverfasser:	Malyshkin, Y.A., Zhukovskii, M.E.
Format:	Artikel
Sprache:	eng
Schlagworte:	0-1 law Monadic second-order logic Preferential attachment tree Uniform attachment tree
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We prove the monadic second-order 0-1 law for two recursive tree models: uniform attachment tree and preferential attachment tree. We also show that the first order 0-1 law does not hold for non-tree uniform attachment models.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2021.109061