From strings to higher dimensional strings

There are well-known connections between word language theory and semigroup theory, mediated by free monoids, with deep link with the theory of finite state automata. By considering free inverse monoids instead of free monoids and premorphisms into ordered monoids instead of morphisms into monoids, we manage to lift these connections to languages of finite trees and, beyond, towards a more general notion of higher dimensional strings. In this talk, we will give a quick overview of the background results with a special emphasis on the main underlying concepts and methods.

Authors

• David Janin

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