Derivatives of Quantitative Regular Expressions.

Quantitative regular expressions (QREs) have been recently proposed as a high-level declarative language for specifying complex numerical queries over data streams in a modular way. QREs have appealing theoretical properties, and each QRE can be compiled into an efficient streaming algorithm for its evaluation. In this paper, we generalize the notion of Brzozowski derivatives for classical regular expressions to QREs. Such derivatives immediately lead to an algorithm for incremental evaluation of QREs. While this algorithm does not have better time or space complexity than the previously known evaluation technique, it has the benefit of being simpler to explain and easier to prove correct.