Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.

中文翻译：

---

加权重启自动机接受的语言

引入了加权重启自动机来研究重启自动机计算的定量方面。在较早的工作中，我们研究了通过加权重启自动机计算的函数和关系的类。在这里，我们通过附加要求来限制与给定输入单词相关联的权重，从而使用它们来定义形式语言的类别。这样，加权重启自动机可以用作语言接受器。首先，我们表明通过使用相对于热带半环的接受概念，我们可以避免使用辅助符号。此外，事实证明，某种类型的单词加权自动重启等同于不遗忘的自动重启，单词加权重启自动机接受的另一种语言显示为在交集操作下关闭。这是第一个结果，表明在交叉点下，关闭了根据重新启动自动机的相当普通的类别定义的一类语言。最终，我们证明了可以通过常规加权的重启自动机（无法执行此操作）来模拟允许在重写步骤中使用辅助符号并在执行重写步骤后继续读取的重启自动机。