Equivalences of Transition Systems in an Algebraic Framework
We study the category of transition systems and the notions of equivalence by simulation and by bisimulation. In order to study the notion of simulation we introduce a monad on the category of transition systems. Bisimulation is studied in an algebraic way, by introducing a category of algebras which turns out to be the “Stone dual” of the category of transition systems. This category of algebras seems to be a natural framework for reasoning about bisimulation equivalence; in particular we argue an equivalence between the concepts of minimal transition system in a bisimulation class and minimal subalgebra.
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