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Let  q  be an odd prime power and  D  be the set of irreducible polynomials inF    q[  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.

Irreducible compositions of degree two polynomials over finite fields have regular structure