Topological Characterisation of Multi-buffer Simulation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10506)


Multi-buffer simulation is an extension of simulation preorder that can be used to approximate inclusion of languages recognised by Büchi automata up to their trace closures. It has been shown that multi-buffer simulation with unbounded buffers can be characterised with the existence of a continuous function f that witnesses trace closure inclusion. In this paper, we show that such a characterisation can be refined to the case where we only consider bounded buffers by requiring the function f to be Lipschitz continuous. This characterisation only holds for some restricted classes of automata. One of the automata should only produce words where each letter does not commute unboundedly to the left or right. We will show that such an automaton can be characterised with a cyclic-path-connected automaton, which is a refinement of a syntactic characterisation of an automaton that has a regular trace closure.


  1. 1.
    Abdulla, P.A., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T.: Computing simulations over tree automata. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 93–108. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-78800-3_8 CrossRefGoogle Scholar
  2. 2.
    Clerbout, M., Latteux, M.: Semi-commutations. Inf. Comput. 73(1), 59–74 (1987)CrossRefzbMATHGoogle Scholar
  3. 3.
    Dill, D.L., Hu, A.J., Wong-Toi, H.: Checking for language inclusion using simulation preorders. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 255–265. Springer, Heidelberg (1992). doi: 10.1007/3-540-55179-4_25 CrossRefGoogle Scholar
  4. 4.
    Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for Büchi automata. In: Orejas, F., Spirakis, P.G., Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 694–707. Springer, Heidelberg (2001). doi: 10.1007/3-540-48224-5_57 CrossRefGoogle Scholar
  5. 5.
    Finkel, O.: Three applications to rational relations of the high undecidability of the infinite post correspondence problem in a regular \(\omega \)-language. Int. J. Found. Comput. Sci. 23(7), 1481–1498 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fritz, C., Wilke, T.: Simulation relations for alternating Büchi automata. Theor. Comput. Sci. 338(1), 275–314 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Henzinger, T.A., Kupferman, O., Rajamani, S.K.: Fair simulation. Inf. Comput. 173(1), 64–81 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Holtmann, M., Kaiser, L., Thomas, W.: Degrees of lookahead in regular infinite games. Log. Methods Comput. Sci. 8(3) (2012)Google Scholar
  9. 9.
    Hutagalung, M., Hundeshagen, N., Kuske, D., Lange, M., Lozes, É.: Multi-buffer simulations for trace language inclusion. In: GandALF 2016, pp. 213–227 (2016)Google Scholar
  10. 10.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages: Vol. 3: Beyond Words. Springer, New York (1977)Google Scholar
  11. 11.
    Sakarovitch, J.: The “last” decision problem for rational trace languages. In: Simon, I. (ed.) LATIN 1992. LNCS, vol. 583, pp. 460–473. Springer, Heidelberg (1992). doi: 10.1007/BFb0023848 Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of KasselKasselGermany

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