Abstract
We address the problem of reducing the size of (nondeterministic, bottom-up) tree automata using suitable, language-preserving equivalences on the states of the automata. In particular, we propose the so-called composed bisimulation as a new language preserving equivalence. Composed bisimulation is defined in terms of two different relations, namely upward and downward bisimulation. Moreover, we provide simple and efficient algorithms for computing composed bisimulation based on a reduction to the problem of computing bisimulations on transition systems. The proposal of composed bisimulation is motivated by an attempt to obtain an equivalence that can provide better reductions than what currently known bisimulation-based approaches can offer, but which is not significantly more difficult to compute (and hence stays below the computational requirements of simulation-based reductions). The experimental results we present in the paper show that our composed bisimulation meets such requirements, and hence provides users of tree automata with a finer way to resolve the trade-off between the available degree of reduction and its cost.
This work was supported by the French projects ANR-06-SETI-001 AVERISS and RNTL AVERILES, the Czech Grant Agency (projects 102/07/0322, 102/05/H050), the Barrande project 17356TD, and the Czech Ministry of Education by the project MSM 0021630528 Security-Oriented Research in Information Technology.
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Abdulla, P., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T.: Composed Bisimulation for Tree Automata. Technical Report FIT-TR-2008-04, FIT, Brno Uni. of Technology, Czech Republic (2008)
Abdulla, P., Bouajjani, A., Holik, L., Kaati, L., Vojnar, T.: Computing Simulations over Tree Automata: Efficient Techniques for Reducing Tree Automata. In: Proc. of TACAS 2008. LNCS. Springer, Heidelberg (2008)
Abdulla, P., Högberg, J., Kaati, L.: Bisimulation Minimization of Tree Automata. In: Ibarra, O.H., Yen, H.-C. (eds.) CIAA 2006. LNCS, vol. 4094, pp. 173–185. Springer, Heidelberg (2006)
Abdulla, P., Holík, L., Kaati, L., Vojnar, T.: A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata. Technical Report FIT-TR-2008-05, FIT, Brno Uni. of Technology, Czech Republic (2008)
Abdulla, P., Jonsson, B., Mahata, P., d’Orso, J.: Regular Tree Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404. Springer, Heidelberg (2002)
Abdulla, P., Legay, A., d’Orso, J., Rezine, A.: Tree Regular Model Checking: A Simulation-based Approach. The Journal of Logic and Algebraic Programming 69(1-2), 93–121 (2006)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract Regular Tree Model Checking. In: Proc. of INFINITY 2005; ENTCS 149(1) (published, 2006)
Bouajjani, A., Habermehl, P., Rogalewicz, A., Vojnar, T.: Abstract Regular Tree Model Checking. ENTCS 149, 37–48 (2006)
Bouajjani, A., Touili, T.: Extrapolating Tree Transformations. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404. Springer, Heidelberg (2002)
Henzinger, M., Henzinger, T., Kopke, P.: Computing Simulations on Finite and Infinite Graphs. In: Proc. of FOCS 1995. IEEE, Los Alamitos (1995)
Högberg, J., Maletti, A., May, J.: Backward and Forward Bisimulation Minimisation of Tree Automata. In: Holub, J., Žďárek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 109–121. Springer, Heidelberg (2007)
Klarlund, N., Møller, A.: MONA Version 1.4 User Manual, BRICS, Department of Computer Science, University of Aarhus, Denmark (2001)
Paige, R., Tarjan, R.: Three Partition Refinement Algorithms. SIAM Journal on Computing 16, 973–989 (1987)
Ranzato, F., Tapparo, F.: A New Efficient Simulation Equivalence Algorithm. In: Proc. of LICS 2007. IEEE CS, Los Alamitos (2007)
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Abdulla, P.A., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T. (2008). Composed Bisimulation for Tree Automata . In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_22
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DOI: https://doi.org/10.1007/978-3-540-70844-5_22
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