Beyond Register Automata: Pushing the Border of Decidability

Register automaton (RA) operating over infinite alphabet is one of the great tools for pattern matching with backreferences, runtime verification, or modelling of parallel computation. In case of pattern matching with backreferences, the state-of-the-art matchers make use of backtracking algorithms, whose application causes significant slowdown in case of nondeterministic regular expressions. Since RAs cannot always be determinised, it is an unsuitable model for solution to problems related to inefficient usage of backtracking algorithms. On the other hand, the RA's quality of being equipped by a finite memory serves as a good basis for storing the so-called capture groups used in pattern matching with backreferences. In this work, a formal model called register set automaton (RsA) is proposed. A large class of RAs can be transformed into this deterministic model, which, among other things, allows for fast pattern matching with backreferences. We explore RsA's properties including decidability of emptiness testing, determinisability, closure under Boolean operations and we compare it to other register models in context of their expressive power.

finite memory automata, register automata, infinite alphabet, regular expressions, regular expressions with backreferences, language inclusion of register automata