A final coalgebra for k-regular sequences

Hansen, Helle Hvid and Kupke, Clemens and Rutten, Jan and Winter, Joost; van Breugel, Frank and Kashefi, Elham and Palamidessi, Catuscia and Rutten, Jan, eds. (2014) A final coalgebra for k-regular sequences. In: Horizons of the Mind. Springer: Lecture Notes in Computer Science, pp. 363-383. ISBN 978-3-319-06879-4 (https://doi.org/10.1007/978-3-319-06880-0_19)

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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.