Geodesic
A hierarchy of automatic ω-words having a decidable MSO theory
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 417-450

Voir la notice de l'article provenant de la source Numdam

We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSO-interpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above mentioned definability and decidability properties. We introduce k-lexicographic presentations, and morphisms of level k stacks and show that these are inter-translatable, thus giving rise to the same classes of k-lexicographic or level k morphic words. We prove that these presentations are also canonical, which implies decidability of the MSO theory of every k-lexicographic word as well as closure of these classes under MSO-definable recolorings, e.g. closure under deterministic sequential mappings. The classes of k-lexicographic words are shown to constitute an infinite hierarchy.

DOI : 10.1051/ita:2008008
Classification : 03D05, 68Q42, 68Q45, 68R15
Keywords: morphic words, monadic second-order logic, automatic structures, automatic sequences 
@article{ITA_2008__42_3_417_0,
     author = {B\'ar\'any, Vince},
     title = {A hierarchy of automatic $\omega $-words having a decidable {MSO} theory},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {417--450},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     doi = {10.1051/ita:2008008},
     mrnumber = {2434027},
     zbl = {1152.03030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2008008/}
}
TY  - JOUR
AU  - Bárány, Vince
TI  - A hierarchy of automatic $\omega $-words having a decidable MSO theory
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2008
SP  - 417
EP  - 450
VL  - 42
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ita:2008008/
DO  - 10.1051/ita:2008008
LA  - en
ID  - ITA_2008__42_3_417_0
ER  - 
%0 Journal Article
%A Bárány, Vince
%T A hierarchy of automatic $\omega $-words having a decidable MSO theory
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2008
%P 417-450
%V 42
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ita:2008008/
%R 10.1051/ita:2008008
%G en
%F ITA_2008__42_3_417_0
Bárány, Vince. A hierarchy of automatic $\omega $-words having a decidable MSO theory. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 417-450. doi: 10.1051/ita:2008008

Cité par Sources :