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Weak index versus Borel rank

Author Filip Murlak

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Filip Murlak

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Filip Murlak. Weak index versus Borel rank. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 573-584, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)


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.
  • Weak index
  • Borel rank
  • deterministic tree automata


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