Sensing as a Complexity Measure

Abstract

The size of deterministic automata required for recognizing regular and \(\omega \)-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 \(\omega \)-regular languages, as well as applications of the study in practice, especially in the monitoring and synthesis of reactive systems.