Rewriting Techniques and Applications
Volume 1232 of the series Lecture Notes in Computer Science pp 217227
Scott's conjecture is true, position sensitive weights
 Samuel M. H. W. PerloFreemanAffiliated withMathematics Institute, University of Warwick
 , Péter PrőhleAffiliated withComputer Science Division, University of St AndrewsDepth of Algebra and Numbertheory, Eötvös Loránd University
Abstract
The classification of total reduction orderings for strings over a 2letter 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 ∞, see [15]. Later we proved the case of positive reals which are well approximable to arbitrary order, see [11], and then the case of \({}^n\sqrt k\) and the case of λ where both of λ and λ^{−1} are algebraic integers, like √5−1/2.
It is a challenging problem, whether there is a reasonably small subset G \(\subseteq\) a,b ^{*}x a,b ^{*} such that each total reduction ordering ≻ of {a, b}^{*} is uniquely determined by its restriction to G.
 Title
 Scott's conjecture is true, position sensitive weights
 Book Title
 Rewriting Techniques and Applications
 Book Subtitle
 8th International Conference, RTA97 Sitges, Spain, June 2–5, 1997 Proceedings
 Pages
 pp 217227
 Copyright
 1997
 DOI
 10.1007/3540629505_72
 Print ISBN
 9783540629504
 Online ISBN
 9783540690511
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1232
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Authors

 Samuel M. H. W. PerloFreeman ^{(1)}
 Péter Prőhle ^{(2)} ^{(3)}
 Author Affiliations

 1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK
 2. Computer Science Division, University of St Andrews, North Haugh, FIFE, KY16 9SS, St Andrews, Scotland
 3. Depth of Algebra and Numbertheory, Eötvös Loránd University, Múzeum körút 68., H1088, Budapest, Hungary
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