Alternating tree automata

In automata theory, an alternating tree automaton (ATA) is an extension of nondeterministic tree automaton as same as alternating finite automaton extends nondeterministic finite automaton (NFA).

Computational complexity

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

gollark: It's very readable.
gollark: I would just dump the program's data structures directly into a framebuffer.
gollark: Yes, like the lack of pattern matching.
gollark: it could look like `bees::whatever()` or you could import it as `beeoid` if you wanted and get `beeoid::whatever()`.
gollark: That isn't required by an import system which works.

References

  1. 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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