Diophantine properties of real numbers generated by finite automata
  We study some diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the $b$-adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit. 
Boris Adamczewski (ICJ), Julien Cassaigne (IML)