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### The unification problem for one relation Thue Systems [chapter]

Christopher Lynch
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We give an algorithm for the unification problem for a generalization of Thue Systems with one relation. The word problem is a special case.  ...  Every word problem for Thue systems of one relation can be reduced to a simpler word problem which is either known to be solvable or has a different top symbol on the left and right side [3] .  ...  The Word and Unification Problem In this section we give a class of Thue systems which is a generalization of one equation Thue systems.  ...
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### Page 2227 of Mathematical Reviews Vol. , Issue 91D [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Many problems that are undecidable in general have been shown to be decidable for Church-Rosser Thue systems. For an overview see a paper of R. V. Book [J.  ...  From the summary: “In most cases of AC unification our method obviates the need for solving Diophantine equations, and thus avoids one of the bottlenecks of other associative-commutative unification techniques  ...
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### Page 5376 of Mathematical Reviews Vol. , Issue 94i [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We also present the main ideas of an efficient E-unification algorithm based on presentations the conditions of which contain only E-unification problems between variables.”  ...  For ex- ample, presentations based on different kinds of conditions lead to E-unification algorithms the behavior of which depends on the axiom applied.  ...
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### Editorial

Jean-Pierre Jouannaud
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
The paper by Ronald Book synthesises at least ten years of research on Thue Systems, with a particular emphasis on the role of Church-Rosser properties in deciding important questions related to Thue Systems  ...  Unfortunately, the paper leaves open the problem of unification for (left and right) distributivity.  ...
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### An Early Completion Algorithm: Thue's 1914 Paper on the Transformation of Symbol Sequences [chapter]

James F. Power
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
References to Thue's 1914 paper on string transformation systems are based mainly on a small section of that work defining Thue systems.  ...  A closer study of the remaining parts of that paper highlight a number of important themes in the history of computing: the transition from algebra to formal language theory, the analysis of the "computational  ...  Of the many current models of computation, one of the oldest is the Thue system, first specified by Axel Thue 100 years ago [Thu14] .  ...
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### Attributive description formalisms ... and the rest of the world [chapter]

Bernhard Nebel, Gert Smolka
<span title="">1991</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Although the intended applications for terminological logics and feature logics are not identical, and the computational services of systems based on the respective formalisms are quite different for this  ...  In this paper, we will show how attributive description formalisms relate to "the rest of the world."  ...  Acknowledgement We would like to thank Franz Baader and Werner Nutt for a number of helpful comments on an earlier version of this paper.  ...
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### Page 5584 of Mathematical Reviews Vol. , Issue 96i [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author proves that the uniform termina- tion problem is undecidable for length-preserving finite semi-Thue systems having 9 rules.  ...  Existence of a semi-Thue system having 10 rules and with undecidable termination problem is shown. {For the entire collection see MR 96b:68005. } K. G.  ...
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### Page 4866 of Mathematical Reviews Vol. , Issue 2004f [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
; Tsu) The unification problem for confluent right-ground term rewriting systems.  ...  Summary: “The unification problem for term rewriting systems (TRSs) is the problem of deciding, for a given TRS R and two terms M and N, whether there exists a substitution @ such that M@ and NO are congruent  ...
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### Report on 11th International Conference on Rewriting Techniques and Applications (RTA2000) 第11回 書き換え技法と応用国際会議 (RTA2000) 参加報告

Yoshihito Toyama
<span title="">2001</span> <i title="Japan Society for Software Science and Technology"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rb7emmmksfcvpgy56dei5flkne" style="color: black;">Konpyuta sofutowea</a> </i> &nbsp;
Gutierrez, Normal forms and reduction for theories of binary relations • R. Statman, On the Word Problem for Combi- nators • M.  ...  Lohrey, Word Problems and Confluence Problems for Restricted Semi-Thue Systems 4 EXPSPACE • D. Miller, Abstarct Syntax for Variable Binders ) • J. Levy and M.  ...
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### A strict border for the decidability of E-unification for recursive functions [chapter]

Heinz Faßbender, Sebastian Maneth
<span title="">1996</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Acknowledgments We are thankful to Friedrich Otto for pointing out to us the possibility to improve our previous undecidability result by using the modified version of Post's correspondence problem.  ...  We also thank the referees for many helpful comments and suggestions.  ...  In Theorem 3.2 of [Ott86] , the undecidability of the uniform E-unification problem for finite, length-reducing, and confluent Thue systems is proved.  ...
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### Page 1038 of Mathematical Reviews Vol. , Issue 94b [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Book, A note on confluent Thue systems (231-236); C.  ...  Makanina, New systems of defining relations of the braid group (250-256). {Most of the papers are being reviewed individually.}  ...
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### Page 8086 of Mathematical Reviews Vol. , Issue 98M [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “We give a polynomial algorithm solving the problem ‘is S partially confluent on the rational set R?’ for finite, basic, Noetherian semi-Thue systems.  ...  Since the word matching problem is the non-symmetric restriction of the word unification problem, this presents a non- trivial improvement of the recent result that for this type of string- rewriting system  ...
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### Page 6840 of Mathematical Reviews Vol. , Issue 91M [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author derives necessary and sufficient conditions for a Noetherian Thue system to be canonical over a set S.  ...  The pa- per extends theorems on pushout-complements known for several specific categories to elementary toposes. This generalization is based on a categorical approach to binary relations.  ...
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### Page 420 of Mathematical Reviews Vol. , Issue 87a [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
COMPUTER SCIENCE 420 Book, Thue systems as rewriting systems (pp. 63-94); Friedrich Otto, Deciding algebraic properties of monoids presented by finite Church- Rosser Thue systems (pp. 95-106); Stavros  ...  Fortenbacher, An algebraic approach to unification under associativity and commu- tativity (pp. 381-397); Stefan Arnborg and Erik Tidén, Unifica- tion problems with one-sided distributivity (pp. 398-406  ...
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### Page 8181 of Mathematical Reviews Vol. , Issue 99m [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(1-CKSN-CS; Potsdam, NY) The unification problem for one relation Thue systems.  ...  Summary: “We give an algorithm for the unification problem for a generalization of Thue systems with one relation. The word problem is a special case.  ...
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