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Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...
This paper presents a generalized minimal realization theory of machines in a category which contains the Kleiski case. The minimal realization is the cheapest realization for a given cost functor. The final reachable realization of Arbib and Manes ([5]) and the minimal state approach for nondeterministic machines are included here.
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