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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Černý, J., Pirická, A., Rosenauerová, B.: On directable automata. Kybernetika 7(4), 289–298 (1971)
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)
Eppstein, D.: Reset sequences for monotonic automata. SIAM Journal on Computing 19(3), 500–510 (1990)
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)
Kari, J.: Synchronizing and Stability of Finite Automata. Journal of Universal Computer Science 8, 270–277 (2002)
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)
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)
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)
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)
Podolak, I.T.: Hierarchical Classifier with Overlapping Class Groups. Expert Systems with Applications 34(1), 673–682 (2008)
Podolak, I.T., Roman, A.: A new notion of weakness in classification theory. Advances in Intelligent and Soft Computing 57, 239–245 (2009)
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)
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)
Pomeranz, I., Reddy, S.M.: On synchronizing sequences and test sequence partitioning. In: Proc. IEEE 16th VLSI Test Symp., pp. 158–167 (1998)
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)
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)
Trahtman, A.N.: The road coloring problem. Israel Journal of Mathematics 1(172), 51–60 (2009)
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)
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)
Volkov, M.V.: Exponents of labeled digraphs and synchronizing automata. In: First Russian-Finish Symposium on Discrete Mathematics (2011) (not published)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)