Adaptive Non-linear Pattern Matching Automata

Abstract

Efficient pattern matching is fundamental for practical term rewrite engines.By preprocessing the given patterns into a finite deterministic automaton thematching patterns can be decided in a single traversal of the relevant parts ofthe input term. Most automaton-based techniques are restricted to linearpatterns, where each variable occurs at most once, and require an additionalpost-processing step to check so-called variable consistency. However, we canshow that interleaving the variable consistency and pattern matching phases canreduce the number of required steps to find all matches. Therefore, we take theexisting adaptive pattern matching automata as introduced by Sekar et al andextend these with consistency checks. We prove that the resulting deterministicpattern matching automaton is correct, and show several examples where somereduction can be achieved