Abstract
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that for a given deterministic bottom-up tree automaton it can be decided in quadratic time whether or not its language can be recognized by a DTA. Since there are finite tree languages that cannot be recognized by DTAs, we also consider finite unions of DTAs and show that also here, definability within deterministic bottom-up tree automata is decidable in quadratic time.
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Acknowledgment
We are grateful to Wim Martens, Helmut Seidl, Magnus Steinby, and Martin Lange for pointing us to some of the literature.
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Leupold, P., Maneth, S. (2021). Deciding Top-Down Determinism of Regular Tree Languages. In: Bampis, E., Pagourtzis, A. (eds) Fundamentals of Computation Theory. FCT 2021. Lecture Notes in Computer Science(), vol 12867. Springer, Cham. https://doi.org/10.1007/978-3-030-86593-1_24
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DOI: https://doi.org/10.1007/978-3-030-86593-1_24
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