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Kleene and Büchi theorems for weighted forest languages over M-monoids
Information and Computation ( IF 1 ) Pub Date : 2021-05-17 , DOI: 10.1016/j.ic.2021.104765
Frederic Dörband

We consider forests as tuples of trees and introduce weighted forest automata (wfa) over M-monoids. A wfa acts on each individual tree in a forest like a weighted tree automaton over the same M-monoid. In order to combine the values of trees in forests, a wfa uses an associative multiplication operation that distributes over the addition of the M-monoid. We continue by introducing two semantics for wfa, an “initial algebra”-like semantic and a run-semantic, and prove that these semantics are equal for distributive M-monoids. We prove that our automaton model accepts finite products of recognizable weighted tree languages over M-monoids. Next, we introduce rational weighted forest expressions and forest M-expressions over M-monoids and show that the classes of languages generated by these formalisms coincide with recognizable weighted forest languages under certain conditions on the underlying M-monoid.



中文翻译:

M-monoids 上加权森林语言的 Kleene 和 Büchi 定理

我们将森林视为树的元组,并在 M-monoids 上引入加权森林自动机 (wfa)。wfa 作用于森林中的每一棵树,就像在同一个 M-monoid 上的加权树自动机一样。为了组合森林中树木的值,wfa 使用关联乘法运算,该运算分布在 M-monoid 的加法上。我们继续为 wfa 引入两个语义,一个“初始代数”类语义和一个运行语义,并证明这些语义对于分布式 M-幺半群是相等的。我们证明我们的自动机模型接受 M-monoids 上可识别加权树语言的有限乘积。下一个,

更新日期:2021-05-17
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