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arXiv · 2107.03174

Deciding Top-Down Determinism of Regular Tree Languages

Peter Leupold·Sebastian Maneth
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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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Peter Leupold, Sebastian Maneth. 2021-07-07. Deciding Top-Down Determinism of Regular Tree Languages. https://arxiv.org/abs/2107.03174

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