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Can I read The Word Problem for One-relation Monoids: a Survey on EtoBox?
The Word Problem for One-relation Monoids: a Survey by Carl-Fredrik Nyberg-Brodda is a Computer Science article available to read on EtoBox.
What is The Word Problem for One-relation Monoids: a Survey about?
This survey is intended to provide an overview of one of the oldest and most celebrated open problems in combinatorial algebra: the word problem for one-relation monoids. We provide a history of the problem starting in 1914, and give a detailed overview of the proofs of central results, especially those due to Adian and his student Oganesian. After showing how to reduce the problem to the left cancellative case, the second half of the survey focuses on various methods for solving partial cases in this family. We finish with some modern and very recent results pertaining to this problem, including a link to the Collatz conjecture. Along the way, we emphasise and address a number of incorrect and inaccurate statements that have appeared in the literature over the years. We also fill a gap in the proof of a theorem linking special inverse monoids to one-relation monoids, and slightly strengthen the statement of this theorem. 5 Adian [9, p.294] has made a brief remark to the same effect. 6 Thue, with remarkable foresight, also provides some examples (see [171, §VIII]) of other solvable word problems using what is clearly recognisable as a prototypical form of the Knuth-Bendix completio
Who reads The Word Problem for One-relation Monoids: a Survey?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- Carl-Fredrik Nyberg-Brodda
- Publisher
- Springer Science and Business Media LLC
- Published
- 2021
- Language
- EN
- Field
- Computer Science (Physical Sciences)