UNSPECIFIED (1997) Scott's conjecture is true, position sensitive weights. In: 8th International Conference on Rewriting Techniques and Applications, JUN 02-05, 1997, STIGES, SPAIN.

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Abstract

The classification of total reduction orderings for strings over a 2-letter alphabet w.r.t. monoid presentations with 2 generators was published by U. Martin, see [9], and used the hypothetical truth of Scott's conjecture, which was 3 years old in 1996. Now the results due to Ursula Martin and Elizabeth Scott are completed with the truth of Scott's conjecture. The final proof is simple, but we had difficulties. E. Scott proved the case, when some invariant takes the value either 0, or a positive rational or infinity, see [15]. Later we proved the case of positive reals which are well approximable to arbitrary order, see [11], and then the case of (n) root k and the case of lambda where both of lambda and lambda(-1) are algebraic integers, like root 5 - 1 / 2 It is a challenging problem, whether there is a reasonably small subset G subset of or equal to {a, b}* x {a, b}* such that each total reduction ordering > of {a, b}* is uniquely determined by its restriction to G.

Item Type:	Conference Item (UNSPECIFIED)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Series Name:	LECTURE NOTES IN COMPUTER SCIENCE
Journal or Publication Title:	REWRITING TECHNIQUES AND APPLICATIONS
Publisher:	SPRINGER-VERLAG BERLIN
ISBN:	3-540-62950-5
ISSN:	0302-9743
Editor:	Comon, H
Date:	1997
Volume:	1232
Number of Pages:	11
Page Range:	pp. 217-227
Publication Status:	Published
Title of Event:	8th International Conference on Rewriting Techniques and Applications
Location of Event:	STIGES, SPAIN
Date(s) of Event:	JUN 02-05, 1997
URI:	http://wrap.warwick.ac.uk/id/eprint/15681

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