Abstract
We give a survey of a function-analytic approach in the study of primitivity of matrix families and of synchronizing automata. Then we define the m-synchronising automata and prove that the existence of a reset m-tuple of a deterministic automata with n states can be decided in less than \(m n^2 \bigl (\log _2 n + \frac{m+4}{2}\bigr )\) operations. We study whether the functional-analytic approach can be extended to m-primitivity and to m-synchronising automata. Several open problems and conjectures concerning the length of m-reset tuples, m-primitive products and finding those objects algorithmically are formulated.
The research is supported by FRBR grants 17-01-00809 and 19-04-01227.
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Protasov, V.Y. (2019). Primitivity and Synchronizing Automata: A Functional Analytic Approach. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_2
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