加权交替树自动机
Weighted Alternating Tree Automata
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中文总结 AI 辅助
该研究在交换半环上定义加权交替树自动机，证明其表达能力在半环局部有限时与加权树自动机等价，并将其定义的加权树语言类刻画为可识别加权树语言在逆树同态下的闭包。
中文摘要 AI 辅助
我们在交换半环上定义了加权交替树自动机，它是加权（非交替）树自动机、（非加权）交替树自动机和加权交替（串）自动机的推广。我们研究了其表达能力，证明当所用半环是局部有限时，其表达能力与加权树自动机完全等价。在主要结果中，我们将加权交替树自动机定义的加权树语言类刻画为可识别加权树语言在逆树同态下的闭包。
英文摘要
We define weighted alternating tree automata — a generalization of weighted (non-alternating) tree automata, (unweighted) alternating tree automata, and weighted alternating (string) automata — over commutative semirings. We study their expressive power, and show that it is equivalent to that of weighted tree automata exactly when the employed semiring is locally finite. In our main result, we characterize the class of weighted tree languages defined by weighted alternating tree automata as the closure of the recognizable weighted tree languages under inverse tree homomorphisms.
