关于一阶树可定义集测度的计算

CoRR Pub Date : 2018-09-07 DOI:10.4204/EPTCS.277.15
Marcin Przybylko
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引用次数: 2

摘要

考虑无限二叉树的正则语言测度的计算问题。虽然一般情况仍未解决,但我们证明了由没有后代关系的一阶公式或由连接查询(具有后代关系)的布尔组合定义的语言的度量是合理的和可计算的。此外,我们提供了一个使用后代关系的一阶公式的例子,并定义了具有非理性测度的无限树的语言。
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On Computing the Measures of First-Order Definable Sets of Trees
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.
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