WoLLIC 2003 Preliminary Version Gap Embedding for Well-Quasi-Orderings 1
Download:
by Nachum Dershowitz, Iddo Tzameret
http://www.cs.tau.ac.il/%7Enachumd/papers/Wqo-wollic.pdf
Add To MetaCart
Abstract:
Given a quasi-ordering of labels, a labelled ordered tree s is embedded with gaps in another tree t if there is an injection from the nodes of s into those of t that maps each edge in s to a unique disjoint path in t with greater-or-equivalent labels, and which preserves the order of children. We show that finite trees are well-quasiordered with respect to gap embedding when labels are taken from an arbitrary well-quasi-ordering such that each tree path can be partitioned into a bounded number of subpaths of comparable nodes. This extends Kˇríˇz’s result [3] and is also optimal in the sense that unbounded incomparability yields a counterexample. 1
Citations
| 237 | Orderings for term rewriting systems – Dershowitz - 1982 |
| 168 | Ordering by divisibility in abstract algebras – Higman - 1952 |
| 85 | the Tree Theorem, and Vazsonyi's conjecture – Well-quasi-ordering - 1960 |
| 45 | On well-quasi-ordering finite trees – Nash-Williams - 1963 |
| 27 | Nonprovability of certain combinatorial properties of finite trees – Simpson - 1985 |
| 5 | On the theory of quasi-ordinal diagrams – Okada, Takeuti - 1985 |
| 4 | Well-quasiordering finite trees with gap-condition. Proof of Harvey Friedman’s conjecture – Kˇríˇz - 1989 |
| 3 | Proving termination for term rewriting systems – Weiermann - 1991 |
