Abstract
We investigate means of efficient computation of the simulation relation over symbolic finite automata (SFAs), i.e., finite automata with transitions labeled by predicates over alphabet symbols. In one approach, we build on the algorithm by Ilie, Navaro, and Yu proposed originally for classical finite automata, modifying it using the so-called mintermisation of the transition predicates. This solution, however, generates all Boolean combinations of the predicates, which easily causes an exponential blowup in the number of transitions. Therefore, we propose two more advanced solutions. The first one still applies mintermisation but in a local way, mitigating the size of the exponential blowup. The other one focuses on a novel symbolic way of dealing with transitions, for which we need to sacrifice the counting technique of the original algorithm (counting is used to decrease the dependency of the running time on the number of transitions from quadratic to linear). We perform a thorough experimental evaluation of all the algorithms, together with several further alternatives, showing that all of them have their merits in practice, but with the clear indication that in most of the cases, efficient treatment of symbolic transitions is more beneficial than counting.
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Notes
- 1.
When describing an algorithm that works over an SFA, we use the notation
to represent the set \({\llbracket {\varDelta }\rrbracket }(q,a)\cap Sim (r)\), i.e., it refers to the concrete transitions of \(\llbracket {\varDelta }\rrbracket \). - 2.
There are still some cases when bisimulation achieved a larger reduction than simulation, which may seem unintuitive since the largest bisimulation is always contained in the simulation preorder. This may happen, e.g., when a simulation-based reduction disables an (even greater) reduction on the subsequent reversed SFA.
to represent the set References
Watson, B.W.: Implementing and Using Finite Automata Toolkits. Cambridge University Press, New York (1999)
Veanes, M., Bjørner, N.: Symbolic automata: the toolkit. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 472–477. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28756-5_33
Veanes, M.: Applications of symbolic finite automata. In: Konstantinidis, S. (ed.) CIAA 2013. LNCS, vol. 7982, pp. 16–23. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39274-0_3
D’Antoni, L., Veanes, M.: The power of symbolic automata and transducers. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 47–67. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_3
Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When simulation meets antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12002-2_14
Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: Proceeding of POPL’13, ACM (2013)
Ilie, L., Navarro, G., Yu, S.: On NFA reductions. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds.) Theory Is Forever. LNCS, vol. 3113, pp. 112–124. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27812-2_11
Holík, L., Šimáček, J.: Optimizing an LTS-simulation algorithm. In: Masaryk, U. (ed.) Proceedings of MEMICS’09 (2009)
Lengál, O., Šimáček, J., Vojnar, T.: VATA: a library for efficient manipulation of non-deterministic tree automata. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 79–94. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28756-5_7
Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: Proceedings of FOCS’95, IEEE (1995)
Cécé, G.: Foundation for a series of efficient simulation algorithms. In: Proceedings of LICS’17, IEEE (2017)
D’Antoni, L., Veanes, M.: Minimization of symbolic automata. In: Proceedings of POPL’14, ACM (2014)
D’Antoni, L., Veanes, M.: Forward bisimulations for nondeterministic symbolic finite automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 518–534. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_30
Eberl, M.: Efficient and verified computation of simulation relations on NFAs. Bachelor’s thesis, TU Munich, 2012
Regular expression library. http://regexlib.com/
Comon, H., et al.: Tree automata techniques and applications (2007)
Elgaard, J., Klarlund, N., Møller, A.: MONA 1.x: new techniques for WS1S and WS2S. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 516–520. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0028773
Fiedor, T., Holík, L., Lengál, O., Vojnar, T.: Nested antichains for WS1S. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 658–674. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_59
Ranzato, F.: A more efficient simulation algorithm on Kripke structures. In: Chatterjee, K., Sgall, J. (eds.) MFCS 2013. LNCS, vol. 8087, pp. 753–764. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40313-2_66
Bustan, D., Grumberg, O.: Simulation-based minimization. ACM Trans. Comput. Log. 4(2), 181–206 (2003)
Holík, L., Lengál, O., Síč, J., Veanes, M., Vojnar, T.: Simulation algorithms for symbolic automata (Technical Report). CoRR, arXiv:abs/1807.08487 (2018)
Acknowledgements
This paper was supported by the Czech Science Foundation projects 16-17538S and 16-24707Y, the IT4IXS: IT4Innovations Excellence in Science project (LQ1602), and the FIT BUT internal project FIT-S-17-4014.
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Holík, L., Lengál, O., Síč, J., Veanes, M., Vojnar, T. (2018). Simulation Algorithms for Symbolic Automata. In: Lahiri, S., Wang, C. (eds) Automated Technology for Verification and Analysis. ATVA 2018. Lecture Notes in Computer Science(), vol 11138. Springer, Cham. https://doi.org/10.1007/978-3-030-01090-4_7
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