Efficient inclusion checking on explicit and semi-symbolic tree automata

Authors:
Lukáš Holík;Ondřej Lengál;Jiří Šimáček;Tomáš Vojnar
Affiliations:
FIT, Brno University of Technology, Czech Republic and Uppsala University, Sweden;FIT, Brno University of Technology, Czech Republic;FIT, Brno University of Technology, Czech Republic and VERIMAG, UJF, CNRS, INPG, Gières, France;FIT, Brno University of Technology, Czech Republic
Venue:
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Year:
2011

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Abstract

The paper considers several issues related to efficient use of tree automata in formal verification. First, a new efficient algorithm for inclusion checking on non-deterministic tree automata is proposed. The algorithm traverses the automaton downward, utilizing antichains and simulations to optimize its run. Results of a set of experiments are provided, showing that such an approach often very significantly outperforms the so far common upward inclusion checking. Next, a new semi-symbolic representation of non-deterministic tree automata, suitable for automata with huge alphabets, is proposed together with algorithms for upward as well as downward inclusion checking over this representation of tree automata. Results of a set of experiments comparing the performance of these algorithms are provided, again showing that the newly proposed downward inclusion is very often better than upward inclusion checking.