// Workers AI · dad joke modeDoes Alternating tree automata go to parties? It branches out.

In automata theory, an alternating tree automaton (ATA) is a generalisation of a nondeterministic tree automaton in the same way that an alternating finite automaton is a generalisation of a nondeterministic finite automaton (NFA).

Computational complexity

The emptiness problem (deciding whether the language of an input ATA is empty) for ATAs, and therefore its complement, the universality problem, are EXPTIME-complete.^[1] The membership problem (testing whether an input tree is accepted by an input AFA) is in PTIME^[1].

References

1 2 H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison et M. Tommasi, Tree Automata Techniques and Applications (Theorem 7.5.1 and subsequent remark)

P ≟ NP

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[comon2008tree-1] 1 2 H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison et M. Tommasi, Tree Automata Techniques and Applications (Theorem 7.5.1 and subsequent remark)

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