We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams: by finite dimensional linear systems; by finite stream circuits; by finite weighted stream automata; and by finite dimensional subsystems of the set of streams.
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Int. Fed. of Computational Logic
Logical Methods in Computer Science
Computer Security

Rutten, J. (2008). Rational streams coalgebraically. Logical Methods in Computer Science, 4(3).