An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is $k\in \mathbb{N}$, such that for every input it has at most k accepting computations. We consider nondeterministic Büchi automata (NBA) over infinite trees and prove that it is decidable in polynomial time, whether an automaton is unambiguous, boundedly ambiguous, finitely ambiguous, or countably ambiguous.

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关于 Büchi 树自动机的模糊度

如果自动机对于每个输入最多有一个接受计算，则它是明确的。如果自动机对于每个输入最多具有有限（分别，可数）许多接受计算，则它是有限（分别，可数）模糊的。一个自动机是有界模糊的，如果有$克\in \mathbb{N}$，这样对于每个输入它最多有k 个接受计算。我们在无限树上考虑非确定性 Büchi 自动机 (NBA)，并证明它在多项式时间内是可判定的，无论自动机是明确的、有界模糊的、有限模糊的还是可数模糊的。