The Subword Reversing Method

We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating presented (semi)groups. In particular, it leads to cancellativity and embeddability criteria for monoids and to efficient solutions for the word problem of monoids and groups of fractions. Subword reversing is a combinatorial method for investigating presented semigroup. It has been developed in various contexts and the results are scattered in different sources [13, 15, 24, 17, 20, 25, 5, ...]. This text is a survey that discusses the main aspects of the method, its range, its uses, and its efficiency. The emphasis is put on the exportable applications rather than on the internal technicalities, for which we refer to literature. New examples and open questions are mentioned, as well as a few new results. Excepted in the cases where no reference is a...

• Type: Journal
• Year: 2011
• Where: IJAC
• Authors: Patrick Dehornoy
• Keywords: Combinatorial Method, IJAC 2011, Preferred Direction, Word Problem