Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic omega-automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition.

中文翻译：

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欧米茄常规语言的近似自动机

无限单词上的自动机，也称为欧米茄自动机，在反应系统的验证和综合中起关键作用。Ω自动机的频谱由两个特征定义：接受条件（例如Buchi或奇偶校验）和自动机的确定性（例如确定性或非确定性），这些特征在自动机理论的应用中起着至关重要的作用。例如，某些接受条件可以通过专用工具和算法比其他条件更有效地处理；此外，某些应用程序（例如综合和概率模型检查）要求将属性表示为某种类型的确定性自动机，但是，这些属性不能总是由具有所需接受条件和确定性的自动机表示。在本文中，我们研究了给定类中通过自动机逼近线性时间属性的问题。我们的近似基于将语言保留到用户定义的精度，这取决于保留的无​​限执行的有限套索表示的大小。我们研究了不同类型的逼近自动机的状态复杂度，并提供了在不同自动机类中进行逼近的构造，例如，用一个简单的接受条件将一个给定的自动机逼近。