Efficient Inclusion Checking on Explicit and Semi-symbolic Tree Automata
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.
KeywordsBoolean Function Sink Node Binary Decision Diagram Tree Automaton Simulation Relation
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- 7.Bourdier, T.: Tree Automata-based Semantics of Firewalls. In: Proc. of SAR-SSI 2011. IEEE, Los Alamitos (2011)Google Scholar
- 8.Bryant, R.E.: Graph-based Algorithms for Boolean Function Manipulation. IEEE Trans. Computers (1986)Google Scholar
- 9.Clarke, E.M., McMillan, K.L., Zhao, X., Fujita, M., Yang, J.: Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping. FMSD 10 (1997)Google Scholar
- 12.Holík, L., Lengál, O., Šimáček, J., Vojnar, T.: Efficient Inclusion Checking on Explicit and Semi-Symbolic Tree Automata. Tech. rep. FIT-TR-2011-04, FIT BUT, Czech Rep. (2011)Google Scholar
- 13.Hosoya, H., Vouillon, J., Pierce, B.C.: Regular Expression Types for XML. ACM Trans. Program. Lang. Syst. 27 (2005)Google Scholar
- 15.Klarlund, N., Møller, A., Schwartzbach, M.I.: MONA Implementation Secrets. International Journal of Foundations of Computer Science, 13(4) (2002)Google Scholar
- 16.Madhusudan, P., Parlato, G., Qiu, X.: Decidable Logics Combining Heap Structures and Data. SIGPLAN Not. 46 (2011)Google Scholar
- 17.Somenzi, F.: CUDD: CU Decision Diagram Package Release 2.4.2 (May 2011)Google Scholar