Adaptive Non-linear Pattern Matching Automata

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