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.
翻译：无限单词上的自动自定义, 也称为 omega- automata, 在反应系统的核查和合成中发挥着关键作用。 omerga- automata 的频谱由两个特点来定义: 接受条件( 如 B\\\\\ uchi 或等同) 和自动maton 的确定性( 确定性或非确定性) 。 这些特性在应用自动数据理论中起着关键作用。 例如, 某些接受条件可以通过专门的工具和算法来比其他更高效地处理。 此外, 一些应用程序, 如合成和概率模型检查, 要求属性代表某种类型的确定性 : 接受条件( 如 B\\\ “ uchi 或 等等) 和 确定性( ) 。 然而, 特性不能总是由自动接受条件和确定性( 如确定性) 来代表 。 在本文中, 我们研究一个特定类中, 自动数据适应性特性的问题。 我们的精确度基于保留语言到用户定义精确度的精确度, 以有限的无限期处决的缩略度表示, 以保持一个更精确的排序内 。 我们研究一个自动结构结构的复杂度, 。 提供不同类型, 的精确度, 。
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