On Synchronizing Tree Automata and Their Work–Optimal Parallel Run, Usable for Parallel Tree Pattern Matching

Abstract

We present a way of synchronizing finite tree automata: We define a synchronizing term and a k-local deterministic finite bottom–up tree automaton. Furthermore, we present a work–optimal parallel algorithm for parallel run of the deterministic k-local tree automaton in time with processors, for, or in time with processors, for, where n is the number of nodes of an input tree, on EREW PRAM. Finally, we prove that the deterministic finite bottom–up tree automaton that is used as a standard tree pattern matcher is k-local with respect to the height of a tree pattern.