Well-quasi-ordering hereditarily finite sets

Authors:
Alberto Policriti;Alexandru I. Tomescu
Affiliations:
Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy;Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy and Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania
Venue:
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Year:
2011

Citing 5
Cited 1

Well-structured transition systems everywhere!

Theoretical Computer Science
Graph Minors. XX. Wagner's conjecture

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Graph minors XXIII. Nash-Williams' immersion conjecture

Journal of Combinatorial Theory Series B
A well-quasi-order for tournaments

Journal of Combinatorial Theory Series B
A classification of the expressive power of well-structured transition systems

Information and Computation

Counting extensional acyclic digraphs

Information Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recently, strong immersion was shown to be a well-quasiorder on the class of all tournaments. Hereditarily finite sets can be viewed as digraphs, which are also acyclic and extensional. Although strong immersion between extensional acyclic digraphs is not a wellquasi-order, we introduce two conditions that guarantee this property. We prove that the class of extensional acyclic digraphs corresponding to slim sets (i.e. sets in which every memebership is necessary) of bounded skewness (i.e. sets whose ∈-distance between their elements is bounded) is well-quasi-ordered by strong immersion. Our results hold for sets of bounded cardinality and it remains open whether they hold in general.