Regular languages that can be approximated by testing subword occurrences

Abstract

A language L is said to be regular-measurable if there exists an infinite sequence of pairs of regular languages that “converges” to L. Instead of regular languages, this paper examines measuring power of several fragments of regular languages: piecewise testable (PT) and alphabet testable (AT) languages. In particular, we showed that, while AT-measurability for regular languages is co-NP complete, PT-measurability is decidable in linear time.