Hilbert series of associative algebras and theoretical computer science

Abstract: In this talk we review concepts of theoretical computer science such as unambiguous context-free grammars and regular grammars from the viewpoint of the generating functions of the languages they define.
The Chomsky-Schutzenberger theorem provides a method to compute such series which are respectively algebraic and rational functions.
These notions can applied to study Hilbert series of monomial algebras, that is, associative algebras whose relations are generated by a set of words, that is, a language.
In particular, we introduce the concept of unambiguous context-free monomial algebra by means of the chain languages defining its homology and we prove that its Hilbert series is an algebraic function.