The size of deterministic automata required for recognizing regular and [Formula: see text]-regular languages is a well-studied measure for the complexity of languages. We introduce and study a new complexity measure, based on the sensing required for recognizing the language. Intuitively, the sensing cost quantifies the detail in which a random input word has to be read in order to decide its membership in the language. We study the sensing cost of regular and [Formula: see text]-regular languages, as well as applications of the study in practice, especially in the monitoring and synthesis of reactive systems.

中文翻译：

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传感作为一种复杂性度量

识别常规语言和 [公式：见文本] 常规语言所需的确定性自动机的大小是一种经过充分研究的语言复杂性度量。基于识别语言所需的感知，我们引入并研究了一种新的复杂性度量。直观地说，感知成本量化了必须读取随机输入单词的细节，以便确定其在语言中的成员资格。我们研究了常规语言和 [公式：见正文] 常规语言的感知成本，以及该研究在实践中的应用，特别是在反应系统的监测和综合方面。