On D0L power series

On D0L power series

We study D0L power series. We show how elementary morphisms introduced by Ehrenfeucht and Rozenberg can be used in connection with power series, characterize the sequences of rational numbers and integers which can be appear as coe cients in D0L power series and establish various decidability results. TUCS Research Group Mathematical Structures of Computer Science

On algebraicness of D0L power series

We show that it is decidable whether or not a given D0L power series over a semiring A is A-algebraic in case A = Q+ or A = N. The proof relies heavily on the use of elementary morphisms in a power series framework and gives also a new method to decide whether or not a given D0L language is context-free. Category: F4.3

On sequences defined by D0L power series

We study D0L power series over commutative semirings. We show that a sequence (cn)n 0 of nonzero elements of a eld A is the coe cient sequence of a D0L power series if and only if there exist a positive integer k and integers i for 1 i k such that cn+k = c 1 n+k 1c 2 n+k 2 : : : c k n for all n 0. As a consequence we solve the equivalence problem of D0L power series over computable elds. TUCS R...

On images of D0L and DT0L power series

On the D0L Repetition Threshold

The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean’s Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricte...