Derivative Based Nonbacktracking Real-World Regex Matching with Backtracking Semantics

We develop a new derivative based theory and algorithm for nonbacktracking regex matching that supports anchors and counting, preserves backtracking semantics, and can be extended with lookarounds. The algorithm has been implemented as a new regex backend in .NET and was extensively tested as part of the formal release process of .NET7. We present a formal proof of the correctness of the algorithm, which we believe to be the first of its kind concerning industrial implementations of regex matchers. The paper describes the complete foundation, the matching algorithm, and key aspects of the implementation involving a regex rewrite system, as well as a comprehensive evaluation over industrial case studies and other regex engines.