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Weak index versus Borel rank (0802.2842v1)
Published 20 Feb 2008 in cs.IT and math.IT
Abstract: We investigate weak recognizability of deterministic languages of infinite trees. We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, we propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states. The algorithm works within the time of solving the emptiness problem.