Abstract
We study k-regular sequences from a coalgebraic perspective. Building on the observation that the set of streams over a semiring S can be turned into a final coalgebra, we obtain characterizations of k-regular sequences in terms of finite weighted automata, finite systems of behavioral differential equations, and recognizable power series. The latter characterization is obtained via an isomorphism of final coalgebras based on the k-adic numeration system. © 2014 Springer International Publishing Switzerland.
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CITATION STYLE
Hansen, H. H., Kupke, C., Rutten, J., & Winter, J. (2014). A final coalgebra for k-regular sequences. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8464 LNCS, pp. 363–383). Springer Verlag. https://doi.org/10.1007/978-3-319-06880-0_19
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