Abstract
In this paper we provide an alternative proof of a fundamental theorem by Worrell stating that the (possibly infinite) behaviour of an F-coalgebra state can be faithfully approximated by the collection of its finite, n-step behaviours, provided that F:Set→Set is a finitary set functor. The novelty of our work lies in our proof technique: our proof uses a certain graph game that generalizes Baltag’s F-bisimilarity game. Phrased in terms of games, our main technical result is that behavioural equivalence on F-coalgebras for a finitary set functor F can be captured by a two-player graph game in which at every position a player has only finitely many moves.
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Kupke, C. (2009). Terminal Sequence Induction via Games. In: Bosch, P., Gabelaia, D., Lang, J. (eds) Logic, Language, and Computation. TbiLLC 2007. Lecture Notes in Computer Science(), vol 5422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00665-4_21
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DOI: https://doi.org/10.1007/978-3-642-00665-4_21
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