Affiliation:
1. University of Michigan, Ann Arbor, MI
2. Microsoft Research, Redmond, WA
Abstract
The following known observation is useful in establishing program termination: if a transitive relation
R
is covered by finitely many well-founded relations
U
1
,…,
U
n
then
R
is well-founded. A question arises how to bound the ordinal height |
R
| of the relation
R
in terms of the ordinals α
i
= |
U
i
|. We introduce the notion of the
stature
∥
P
∥ of a well partial ordering
P
and show that |
R
| ≤ ∥α
1
× … × α
n
∥ and that this bound is tight. The notion of stature is of considerable independent interest. We define ∥
P
∥ as the ordinal height of the forest of nonempty bad sequences of
P
, but it has many other natural and equivalent definitions. In particular, ∥
P
∥ is the supremum, and in fact the maximum, of the lengths of linearizations of
P
. And ∥α
1
× … × α
n
∥ is equal to the natural product α
1
⊗ … ⊗ α
n
.
Funder
Division of Mathematical Sciences
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
10 articles.
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