Efficient and Modular Coalgebraic Partition Refinement
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We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, a task arising in different contexts. Coalgebraic generality allows us to not only cover classical relational systems and various forms of weighted systems but way can combine existing system types in various ways. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time O(m· n) where n and m are the numbers of nodes and edges, respectively. The generic complexity results and the possibilities of combining system types is a toolbox for efficient partition refinement algorithms. Instances of our generic algorithm thus match the runtime of the best known algorithms for unlabelled transition systems, Markov chains, and deterministic automata (with fixed alphabets), and improve the best known algorithms for Segala systems.
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