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 \(\mathcal {O}(\log {n})\) time with \(\lceil \frac{n}{\log {n}}\rceil \) processors, for \(k \le \log {n}\), or in \(\mathcal {O}(k)\) time with \(\lceil \frac{n}{k}\rceil \) processors, for \(k \ge \log {n}\), 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.
The authors acknowledge the support of the OP VVV MEYS funded project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”.
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Plachý, Š., Janoušek, J. (2020). On Synchronizing Tree Automata and Their Work–Optimal Parallel Run, Usable for Parallel Tree Pattern Matching. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_47
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