Synchronizing Heuristics for Weakly Connected Automata with Various Topologies

  • Berk CirisciEmail author
  • Barış Sevilmiş
  • Emre Yasin Sivri
  • Poyraz Kıvanç Karaçam
  • Kamer Kaya
  • Hüsnü Yenigün
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 991)


Since the problem of finding a shortest synchronizing sequence for an automaton is known to be NP-hard, heuristics algorithms are used to find synchronizing sequences. There are several heuristic algorithms in the literature for this purpose. However, even the most efficient heuristic algorithm in the literature has a quadratic complexity in terms of the number of states of the automaton, and therefore can only scale up to a couple of thousands of states. It was also shown before that if an automaton is not strongly connected, then these heuristic algorithms can be used on each strongly connected component separately. This approach speeds up these heuristic algorithms and allows them to scale to much larger number of states easily. In this paper, we investigate the effect of the topology of the automaton on the performance increase obtained by these heuristic algorithms. To this end, we consider various topologies and provide an extensive experimental study on the performance increase obtained on the existing heuristic algorithms. Depending on the size and the number of components, we obtain speed-up values as high as 10000x and more.


Finite state automata Synchronizing sequences Strongly connected component 



This work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) [grant number 114E569].


  1. 1.
    Cirisci, B., Kahraman, M.K., Yildirimoglu, C.U., Kaya, K., Yenigun, H.: Using structure of automata for faster synchronizing heuristics. In: Proceedings of the 6th International Conference on Model-Driven Engineering and Software Development, MODELSWARD 2018, Funchal, Madeira - Portugal, pp. 544–551 (2018)Google Scholar
  2. 2.
    Chow, T.S.: Testing software design modelled by finite state machines. IEEE Trans. Softw. Eng. 4, 178–187 (1978)CrossRefGoogle Scholar
  3. 3.
    Eppstein, D.: Reset sequences for monotonic automata. SIAM J. Comput. 19(3), 500–510 (1990)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hierons, R.M., Ural, H.: Optimizing the length of checking sequences. IEEE Trans. Comput. 55(5), 618–629 (2006)CrossRefGoogle Scholar
  5. 5.
    Jourdan, G.V., Ural, H., Yenigün, H.: Reduced checking sequences using unreliable reset. Inf. Process. Lett. 115(5), 532–535 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kudlacik, R., Roman, A., Wagner, H.: Effective synchronizing algorithms. Expert Syst. Appl. 39(14), 11746–11757 (2012)CrossRefGoogle Scholar
  7. 7.
    Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines-a survey. Proc. IEEE 84(8), 1090–1123 (1996)CrossRefGoogle Scholar
  8. 8.
    Roman, A., Szykula, M.: Forward and backward synchronizing algorithms. Expert Syst. Appl. 42(24), 9512–9527 (2015)CrossRefGoogle Scholar
  9. 9.
    Rystsov, I.: Reset words for commutative and solvable automata. Theoret. Comput. Sci. 172(1–2), 273–279 (1997)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Trahtman, A.N.: Some results of implemented algorithms of synchronization. In: 10th Journees Montoises d’Inform (2004)Google Scholar
  11. 11.
    Volkov, M.V.: Synchronizing automata and the Černý conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 11–27. Springer, Heidelberg (2008). Scholar
  12. 12.
    Volkov, M.V.: Synchronizing automata preserving a chain of partial orders. Theoret. Comput. Sci. 410(37), 3513–3519 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Berk Cirisci
    • 1
    Email author
  • Barış Sevilmiş
    • 1
  • Emre Yasin Sivri
    • 1
  • Poyraz Kıvanç Karaçam
    • 1
  • Kamer Kaya
    • 1
  • Hüsnü Yenigün
    • 1
  1. 1.Computer Science and Engineering, Faculty of Engineering and Natural SciencesSabanci UniversityIstanbulTurkey

Personalised recommendations