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Minimization via duality

Bezhanishvili, N. and Kupke, C. and Panangaden, P. (2012) Minimization via duality. In: Logic, Language, Information and Computation. Lecture notes in computer science / Theoretical Computer Science and General Issues, 7456 LNCS . Springer, pp. 191-205. ISBN 9783642326202

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We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object.