Let b ≥ 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.

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An inÿnite word deÿned over a ÿnite alphabet A is balanced if for any pair (!; ! ) of factors of the same length and for any letter a in the alphabetwhere |!|a denotes the number of occurrences of the letter a in the word !. In this paper, we generalize this notion and introduce a measure of balance for an inÿnite sequence. In the case of ÿxed points of primitive substitutions, we show that the asymptotic behaviour of this measure is in part ruled by the spectrum of the incidence matrix associated with the substitution. Connections with frequencies of letters and other balance properties are also discussed.