We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way — for example, the set of all word pairs [Formula: see text] where [Formula: see text] is a prefix of [Formula: see text] independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behavior of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages as well as a decision question about synchronous transducers.

中文翻译：

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字母不变和用户定义标签上的正则表达式和转换器

我们对以字母不变的方式表示单词关系的正则表达式和转换器感兴趣——例如，所有单词对的集合 [Formula: see text] 其中 [Formula: see text] 是 [Formula: see text] 的前缀] 独立于字母表是什么。当前形式语言对象的软件系统没有定义这些对象的机制。我们定义了转换器，其中转换标签涉及我们所谓的集合规范，其中一些是字母不变的。事实上，我们给出了更广泛的自动机类型对象定义，称为标记图，其中每个转换标签可以是任何字符串，只要该字符串表示某个幺半群的子集。然后，标记图的行为是该幺半群的子集。我们对正则表达式做同样的事情。我们在标记图的广泛级别上对普通正则表达式和换能器进行了一些经典算法结构的扩展，并且不会牺牲扩展结构的计算效率。对于具有设定规格的传感器，我们获得了可应用于有关独立常规语言的问题以及有关同步传感器的决策问题的进一步算法。