A Compositional Framework for Controller Synthesis

  • Christel Baier
  • Joachim Klein
  • Sascha Klüppelholz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


Given a system \(\mathcal{A}\) and objective Φ, the general task of controller synthesis is to design a decision making policy that ensures Φ to be satisfied. This paper deals with LTS-like system models and controllers that make their decisions based on the observables of the actions performed so far. Our main contribution is a compositional framework for treating multiple linear-time objectives inductively. For this purpose, we introduce a novel notion of strategies that serve as generators for observation-based decision functions. Our compositional approach will rely on most general (i.e., most permissive) strategies generating all decision functions that guarantee the objective under consideration. Finally we show that for safety and co-safety objectives Φ, most general strategies are realizable by finite-state controllers that exogenously enforce Φ.


General Strategy Decision Function Visible Action Controllable Component Controller Synthesis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable specifications of reactive systems. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 1–17. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  2. 2.
    Asarin, E., Bournez, O., Dang, T., Maler, O., Pnueli, A.: Effective synthesis of switching controllers for linear systems. IEEE Special Issue on Hybrid Systems 88, 1011–1025 (2000)Google Scholar
  3. 3.
    Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S.S. (eds.) HS 1994. LNCS, vol. 999, pp. 1–20. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  4. 4.
    Bernet, J., Janin, D., Walukiewicz, I.: Permissive strategies: From parity games to safety games. ITA 36(3), 261–275 (2002)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Berwanger, D., Doyen, L.: On the power of imperfect information. In: FSTTCS 2008. LIPIcs, vol. 2, pp. 73–82. Schloss Dagstuhl (2008)Google Scholar
  6. 6.
    Bouyer, P., Duflot, M., Markey, N., Renault, G.: Measuring permissivity in finite games. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 196–210. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.F.: Algorithms for omega-regular games with imperfect information. Logical Methods in Computer Science 3(3) (2007)Google Scholar
  8. 8.
    Filiot, E., Jin, N., Raskin, J.F.: Compositional Algorithms for LTL Synthesis. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 112–127. Springer, Heidelberg (2010)Google Scholar
  9. 9.
    Kuijper, W., van de Pol, J.: Compositional control synthesis for partially observable systems. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 431–447. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Kupferman, O., Madhusudan, P., Thiagarajan, P.S., Vardi, M.Y.: Open systems in reactive environments: Control and synthesis. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 92–107. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Mohalik, S., Walukiewicz, I.: Distributed games. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 338–351. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL 1989, pp. 179–190. ACM, New York (1989)Google Scholar
  13. 13.
    Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: LICS 1990, vol. 2, pp. 746–757 (1990)Google Scholar
  14. 14.
    Reif, J.H.: The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29(2), 274–301 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Vardi, M.Y.: An automata-theoretic approach to fair realizability and synthesis. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 267–278. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  16. 16.
    Wonham, W.M.: On the control of discrete-event systems. In: Three Decades of Mathematical System Theory. LNCIS, vol. 135, pp. 542–562. Springer, Heidelberg (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christel Baier
    • 1
  • Joachim Klein
    • 1
  • Sascha Klüppelholz
    • 1
  1. 1.Technische Universität DresdenGermany

Personalised recommendations