Results 1 
5 of
5
Simple Gap Termination for Term Graph Rewriting Systems
 In Theory of Rewriting Systems and Its Application
, 1995
"... This paper proves the extension of KruskalFriedman theorem, which is an extension of the ordinary Kruskal's theorem with gapcondition, on !trees (Main theorem 1 in section 3). Based on the theorem, a new termination criteria for cyclic term graph rewriting systems, named simple gap termination (M ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This paper proves the extension of KruskalFriedman theorem, which is an extension of the ordinary Kruskal's theorem with gapcondition, on !trees (Main theorem 1 in section 3). Based on the theorem, a new termination criteria for cyclic term graph rewriting systems, named simple gap termination (Main theorem 2 in section 4), is proposed where the naive extension of simple termination (based on [Lav78]) does not work well. 1 Introduction A term graph rewriting system (TGRS) has been commonly used from efficiency reasons in implementations of a term rewriting system (TRS), such as CLEAN 1 . A TGRS can be regarded as a TRS with addresses  i.e., a variable in a rule of a TRS is regarded as an address in a TGRS. Thus, subterms will be shared in each reduction step of a TGRS, whereas each reduction step of a TRS simply copies. Theoretical basis for a TGRS has been extensively worked [MSvE94], but the most works have been devoted to a acyclic TGRS. For a cyclic TGRS which can simulate i...
KruskalFriedman Gap . . .
, 2002
"... We investigate new extensions of the KruskalFriedman theorems concerning wellquasiordering of finite trees with the gap condition. For two labelled trees s and t we say that s is embedded with gap into t if there is an injection from the vertices of s into t which maps each edge in s to a unique ..."
Abstract
 Add to MetaCart
We investigate new extensions of the KruskalFriedman theorems concerning wellquasiordering of finite trees with the gap condition. For two labelled trees s and t we say that s is embedded with gap into t if there is an injection from the vertices of s into t which maps each edge in s to a unique path in t with greaterorequal labels. We show that finite trees are wellquasiordered with respect to the gap embedding when the labels are taken from an arbitrary wellquasiordering and each tree path can be partitioned into k ∈ N or less comparable subpaths. This result generalizes both [Kˇrí89] and [OT87], and is also optimal in the sense that unbounded partiality over tree paths yields a counter example.
Phase transitions in Proof Theory
"... Using standard methods of analytic combinatorics we elaborate critical points (thresholds) of phase transitions from provability to unprovability of arithmetical wellpartialordering assertions in several familiar theories occurring in the reverse mathematics program. ..."
Abstract
 Add to MetaCart
Using standard methods of analytic combinatorics we elaborate critical points (thresholds) of phase transitions from provability to unprovability of arithmetical wellpartialordering assertions in several familiar theories occurring in the reverse mathematics program.