Derivative Based Extended Regular Expression Matching Supporting Intersection, Complement and Lookarounds

Abstract: Regular expressions are widely used in software. Various regular expression engines support different combinations of extensions to classical regular constructs such as Kleene star, concatenation, nondeterministic choice (union in terms of match semantics). The extensions include e.g. anchors, lookarounds, counters, backreferences. The properties of combinations of such extensions have been subject of active recent research. In the current paper we present a symbolic derivatives based approach to finding matches to regular expressions that, in addition to the classical regular constructs, also support complement, intersection and lookarounds (both negative and positive lookaheads and lookbacks). The theory of computing symbolic derivatives and determining nullability given an input string is presented that shows that such a combination of extensions yields a match semantics that corresponds to an effective Boolean algebra, which in turn opens up possibilities of applying various Boolean logic rewrite rules to optimize the search for matches. In addition to the theoretical framework we present an implementation of the combination of extensions to demonstrate the efficacy of the approach accompanied with practical examples.