Irreducible compositions of degree two polynomials over finite fields have regular structure
Andrea Ferraguti, Giacomo Micheli, Reto Schnyder · The Quarterly Journal of Mathematics · 2018
Let q be an odd prime power and D be the set of irreducible polynomials in Fq[x] which can be written as a composition of degree two polynomials. In this paper, we prove that D has a natural regular structure by showing that there exists a finite automaton having D as accepted language. Our method is constructive.