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Scott's conjecture is true, position sensitive weights
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UNSPECIFIED (1997) Scott's conjecture is true, position sensitive weights. In: 8th International Conference on Rewriting Techniques and Applications, STIGES, SPAIN, JUN 02-05, 1997. Published in: REWRITING TECHNIQUES AND APPLICATIONS, 1232 pp. 217-227. ISBN 3-540-62950-5. ISSN 0302-9743.
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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) | ||||
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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 | ||||
Official Date: | 1997 | ||||
Dates: |
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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 |
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