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Application of Hierarchical Classifier to Minimal Synchronizing Word Problem

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Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

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Abstract

We present a practical application of Hierarchical Classifier with overlapping clusters to the problem of finding the minimal synchronizing word length of a given finite automaton. We compare our approach with a single neural network model. Using a certain representation of automaton as the classifier’s input we improve HC efficiency and we are able to analyze the relation between particular automata features and minimal synchronizing lengths.

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References

  1. Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.): Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005)

    Book  MATH  Google Scholar 

  2. Černý, J., Pirická, A., Rosenauerová, B.: On directable automata. Kybernetika 7(4), 289–298 (1971)

    MathSciNet  MATH  Google Scholar 

  3. Deshmukh, R.G., Hawat, G.N.: An algorithm to determine shortest length distinguishing, homing, and synchronizing sequences for sequential machines. In: Proc. Southcon 1994 Conference, pp. 496–501 (1994)

    Google Scholar 

  4. Eppstein, D.: Reset sequences for monotonic automata. SIAM Journal on Computing 19(3), 500–510 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fukada, A., Nakata, A., Kitamichi, J., Higashino, T., Cavalli, A.: A conformance testing method for communication protocols modeled as concurrent DFSMs. Treatment of non-observable non-determinism. In: Proc. IEEE 15th Int. Conf. on Information Networking, pp. 155–162 (2001)

    Google Scholar 

  6. Kari, J.: Synchronizing and Stability of Finite Automata. Journal of Universal Computer Science 8, 270–277 (2002)

    MathSciNet  Google Scholar 

  7. Klyachko, A.A., Rystsov, I., Spivak, M.A.: An extremal combinatorial problem associated with the bound on the length of a synchronizing word in an automaton. Kybernetika 2, 16–20 (1987)

    MathSciNet  Google Scholar 

  8. Natarajan, B.K.: An Algorithmic Approach to the Automated Design of Part Orienters. In: Proc. IEEE Symp. Foundations of Computer Science (FOCS 1986), pp. 132–142 (1986)

    Google Scholar 

  9. Olschewski, J., Ummels, M.: The Complexity of Finding Reset Words in Finite Automata. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 568–579. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Pixley, C., Jeong, S.W., Hachtel, G.D.: Exact calculation of synchronizing sequences based on binary decision diagrams. In: Proc. ACM/IEEE 29th Design Automation Conference, pp. 620–623 (1992)

    Google Scholar 

  11. Podolak, I.T.: Hierarchical Classifier with Overlapping Class Groups. Expert Systems with Applications 34(1), 673–682 (2008)

    Article  Google Scholar 

  12. Podolak, I.T., Roman, A.: A new notion of weakness in classification theory. Advances in Intelligent and Soft Computing 57, 239–245 (2009)

    Article  Google Scholar 

  13. Podolak, I.T., Bartocha, K.: A Hierarchical Classifier with Growing Neural Gas Clustering. In: Kolehmainen, M., Toivanen, P., Beliczynski, B. (eds.) ICANNGA 2009. LNCS, vol. 5495, pp. 283–292. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Podolak, I.T., Roman, A.: Fusion of supervised and unsupervised training methods for a multi-class classification problem. Pattern Analysis and Applications 14(4), 395–413 (2011)

    Article  Google Scholar 

  15. Pomeranz, I., Reddy, S.M.: On synchronizing sequences and test sequence partitioning. In: Proc. IEEE 16th VLSI Test Symp., pp. 158–167 (1998)

    Google Scholar 

  16. Ponce, A.M., Csopaki, G., Tarnay, K.: Formal specification of conformance testing documents for communication protocols. In: 5th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC 1994), vol. 4, pp. 1167–1172 (1994)

    Google Scholar 

  17. Roman, A.: Genetic Algorithm for Synchronization. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 684–695. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Trahtman, A.N.: The road coloring problem. Israel Journal of Mathematics 1(172), 51–60 (2009)

    Article  MathSciNet  Google Scholar 

  19. Trahtman, A.N.: An Efficient Algorithm Finds Noticeable Trends and Examples Concerning the Černy Conjecture. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 789–800. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Ananichev, D.S., Volkov, M.V.: Synchronizing Monotonic Automata. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 270–382. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  21. Volkov, M.V.: Exponents of labeled digraphs and synchronizing automata. In: First Russian-Finish Symposium on Discrete Mathematics (2011) (not published)

    Google Scholar 

  22. Zhao, Y., Liu, Y., Guo, X., Zhang, C.: Conformance testing for IS-IS protocol based on E-LOTOS. In: IEEE Int. Conf. on Information Theory and Information Security (ICITIS 2010), pp. 54–57 (2010)

    Google Scholar 

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Podolak, I.T., Roman, A., Jędrzejczyk, D. (2012). Application of Hierarchical Classifier to Minimal Synchronizing Word Problem. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_49

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  • DOI: https://doi.org/10.1007/978-3-642-29347-4_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

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