On the group of a rational maximal bifix code

A code is a set of words that freely generates a free submonoid of the free monoid. A specially relevant place in the theory of codes is occupied by the maximal bifix codes.

In the last years, attention has been given to a process of "localization" in which one looks at the intersection of a code with a language of some special type. To each rational code one associates in a natural way a special finite group that is one of the most relevant parameters in the study of rational bifix codes. In this talk, we present some results concerning the effects produced on this group by the  aforementioned process of localization. We emphasize the methodology that we used, based on recent achievements concerning the structure of free profinite monoids.

Joint work with Jorge Almeida, Revekka Kyriakoglou and Dominique Perrin.

Date and Venue

Start Date
Room FC1 030, DMat-FCUP
End Date


Alfredo Costa

Speaker's Institution




Semigroups, Automata and Languages