Abstract
In this paper, we introduce a notion of a right-sequential function on infinite words. The main result is that any rational function is the composition of a right-sequential function and a left-sequential function. This extends a classical result of Elgot and Mezei on finite words to infinite words. We also show that our class of right-sequential functions includes the normalization of real numbers in some base and the truth value of linear temporal logic. Finally, we apply the decomposition theorem to show that automatic sequences are preserved by rational letter-to-letter functions. © 2010 Springer-Verlag.
Cite
CITATION STYLE
Carton, O. (2010). Right-sequential functions on infinite words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6072 LNCS, pp. 96–106). Springer Verlag. https://doi.org/10.1007/978-3-642-13182-0_9
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