On Critical Exponents in Fixed Points of Non-erasing Morphisms

Let be an alphabet of size t, let f : be a non-erasing morphism, let w be an infinite fixed point of f, and let E(w) be the critical exponent of w. We prove that if E(w) is finite, then for a uniform f it is rational, and for a non-uniform f it lies in the field extension Q[r, 1, . . . , ], where r, 1, . . . , are the eigenvalues of the incidence matrix of f. In particular, E(w) is algebraic of degree at most t. Under certain conditions, our proof implies an algorithm for computing E(w). Key words: Critical exponent; Circular D0L languages

• Type: Conference
• Year: 2006
• Where: DLT
• Authors: Dalia Krieger
• Keywords: Critical Exponent, DLT 2006, DLT 2007, Infinite Fixed Point, Non-erasing Morphism