Abstract This note characterizes those quasi-orderings (A,⪯) for which ( P (A),⊑) are well quasi-orderings, where B 1 ⊑B 2 iff (∀y∈B 2 )(∃x∈B 1 ): x⪯y (for B 1 ,B 2 ⫅A ). It turns out that they are those which do not contain the “Rado structure”, hence are ω 2 -well quasi-orderings in other words. A motivation for the question has come from the area of verification of infinite-state systems, where the usefulness of well quasi-orderings has already been recognized. This note suggests that finer notions might be useful as well. In particular, ω 2 -well quasi-orderings illuminate a specific problem related to termination of a reachability algorithm, which has been touched on by Abdulla and Jonsson.
[1]
Alberto Marcone,et al.
Foundations of BQO theory
,
1994
.
[2]
Parosh Aziz Abdulla,et al.
General decidability theorems for infinite-state systems
,
1996,
Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.
[3]
Parosh Aziz Abdulla,et al.
Verifying Networks of Timed Processes (Extended Abstract)
,
1998,
TACAS.
[4]
Philippe Schnoebelen,et al.
Fundamental Structures in Well-Structured Infinite Transition Systems
,
1998,
LATIN.
[5]
Aziz Abdulla,et al.
Verifying Networks of Timed ProcessesParosh
,
1998
.
[6]
E. C. Milner.
Basic WQO- and BQO-Theory
,
1985
.
[7]
李幼升,et al.
Ph
,
1989
.