Tara Brough
Universidade Nova de Lisboa

Abstract: In semigroups, y is an inverse of x if xyx = x and yxy = y. An inverse monoid is a monoid (semigroup with identity) in which every element has a unique inverse. I will describe the free objects in the category of inverse monoids: for any set X, the free inverse monoid on X is denoted FIM(X). The word problem of a monoid is, informally, the problem of deciding whether two words over a given generating set represent the same element of the monoid. I will explain how this can be considered as a formal language, and discuss the language type (e.g. context-free, context-sensitive) of the word problem of FIM(X) for a finite set X.
The talk will focus primarily on the rank 1 case, in which words over the standard generating set can be viewed as walks in one dimension.