Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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
Clerbout, M., Latteux, M.: Semi-commutations. Inf. Comput. 73(1), 59–74 (1987)
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
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
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)
Fritz, C., Wilke, T.: Simulation relations for alternating Büchi automata. Theor. Comput. Sci. 338(1), 275–314 (2005)
Henzinger, T.A., Kupferman, O., Rajamani, S.K.: Fair simulation. Inf. Comput. 173(1), 64–81 (2002)
Holtmann, M., Kaiser, L., Thomas, W.: Degrees of lookahead in regular infinite games. Log. Methods Comput. Sci. 8(3) (2012)
Hutagalung, M., Hundeshagen, N., Kuske, D., Lange, M., Lozes, É.: Multi-buffer simulations for trace language inclusion. In: GandALF 2016, pp. 213–227 (2016)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages: Vol. 3: Beyond Words. Springer, New York (1977)
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Hutagalung, M. (2017). Topological Characterisation of Multi-buffer Simulation. In: Hague, M., Potapov, I. (eds) Reachability Problems. RP 2017. Lecture Notes in Computer Science(), vol 10506. Springer, Cham. https://doi.org/10.1007/978-3-319-67089-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-67089-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-67088-1
Online ISBN: 978-3-319-67089-8
eBook Packages: Computer ScienceComputer Science (R0)