The Monadic Theory of Morphic Infinite Words and Generalizations

The Monadic Theory of Morphic Infinite Words and Generalizations

On Infinite Terms Having a Decidable Monadic Theory

We study a transformation on terms consisting of applying an inverse deterministic rational mapping followed by an unfolding. Iterating these transformations from the regular terms gives a hierarchy of families of terms having a decidable monadic theory. In particular, the family at level 2 contains the morphic innnite words investigated by Carton and Thomas. We show that this hierarchy coincid...

On the Frequency and Periodicity of Infinite Words On the Frequency and Periodicity of Infinite Words

This work contributes to two aspects of the understanding of infinite words: the frequency of letters in a morphic sequence and periodicity considerations on infinite words. First, we develop a necessary and sufficient criteria for the existence of the frequency of a letter in a morphic sequence, and give some applications of this result. We show that the frequencies of all letters exist in pur...

A Hierarchy of Automatic Words having a Decidable MSO Theory

We investigate automatic presentations of infinite words. Starting points of our study are the works of Rigo and Maes, and Carton and Thomas concerning the lexicographic presentation, respectively the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is canonical in a certain sense. We then go on to gene...

Infinite and Bi-infinite Words with Decidable Monadic Theories

We study word structures of the form (D,<,P ) where D is either N or Z, < is the natural linear ordering on D and P ⊆ D is a predicate on D. In particular we show: (a) The set of recursive ω-words with decidable monadic second order theories is Σ3complete. (b) Known characterisations of the ω-words with decidable monadic second order theories are transfered to the corresponding question for bi-...