拟字母树双态的性质
Properties of quasi-alphabetic tree bimorphisms
摘要：
我们研究类的准字母关系，即，由具有两个准字母树同态和一个正则树语言的树双同态定义的树变换。我们提出了这些关系的规范表示，作为一个直接的后果，我们得到的联合下的封闭。此外，我们表明，他们是不封闭的交叉和补充，并不保留最常见的操作树（分支，子树，v-产品，v-商，f-顶部的连锁）。此外，我们证明了由拟字母树双态定义的翻译是上下文无关字符串语言的乘积。最后，我们提出了准字母关系，字母关系和类树变换定义的几种类型的自顶向下树换能器之间的连接。此外，我们得到准字母关系保持可识别和代数树语言。
英文摘要：
We study the class of quasi-alphabetic relations, i.e., tree transformations defined by tree bimorphisms with two quasi-alphabetic tree homomorphisms and a regular tree language. We present a canonical representation of these relations; as an immediate consequence, we get the closure under union. Also, we show that they are not closed under intersection and complement, and do not preserve most common operations on trees (branches, subtrees, v-product, v-quotient, f-top-catenation). Moreover, we prove that the translations defined by quasi-alphabetic tree bimorphism are exactly products of context-free string languages. We conclude by presenting the connections between quasi-alphabetic relations, alphabetic relations and classes of tree transformations defined by several types of top-down tree transducers. Furthermore, we get that quasi-alphabetic relations preserve the recognizable and algebraic tree languages.
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