Abstract
Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this paper, we use the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (non-deterministic) automata.
The work of Mathias Hülsbusch and Barbara König was partially supported by the DFG project Bevaviour-GT. The work of Alexandra Silva was partially supported by Fundação para a Ciência e a Tecnologia, Portugal, under grant number SFRH/BPD/71956/2010.
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Adámek, J., Bonchi, F., Hülsbusch, M., König, B., Milius, S., Silva, A. (2012). A Coalgebraic Perspective on Minimization and Determinization. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_4
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