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Generalized Rabin(1) Synthesis with Applications to Robust System Synthesis

  • Rüdiger Ehlers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6617)

Abstract

Synthesis of finite-state machines from linear-time temporal logic (LTL) formulas is an important formal specification debugging technique for reactive systems and can quickly generate prototype implementations for realizable specifications.

It has been observed, however, that automatically generated implementations typically do not share the robustness of manually constructed solutions with respect to assumption violations, i.e., they typically do not degenerate nicely when the assumptions in the specification are violated. As a remedy, robust synthesis methods have been proposed. Unfortunately, previous such techniques induced obstacles to their efficient implementation in practice and typically do not scale well.

In this paper, we introduce generalized Rabin(1) synthesis as a solution to this problem. Our approach inherits the good algorithmic properties of generalized reactivity(1) synthesis but extends it to also allow co-Büchi-type assumptions and guarantees, which makes it usable for the synthesis of robust systems.

Keywords

Generalize Reactivity Winning Strategy Recovery Mode Basic Liveness Basic Safety 
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.

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References

  1. 1.
    Alur, R., Henzinger, T.A., Mang, F.Y.C., Qadeer, S., Rajamani, S.K., Tasiran, S.: Mocha: Modularity in model checking. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 521–525. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Madhusudan, P., Nam, W.: Symbolic computational techniques for solving games. STTT 7(2), 118–128 (2005)CrossRefzbMATHGoogle Scholar
  3. 3.
    Arora, A., Gouda, M.G.: Closure and convergence: A foundation of fault-tolerant computing. IEEE Trans. Software Eng. 19(11), 1015–1027 (1993)CrossRefGoogle Scholar
  4. 4.
    Bloem, R., Chatterjee, K., Greimel, K., Henzinger, T.A., Jobstmann, B.: Robustness in the presence of liveness. In: [24], pp. 410–424Google Scholar
  5. 5.
    Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Interactive presentation: Automatic hardware synthesis from specifications: a case study. In: Lauwereins, R., Madsen, J. (eds.) DATE, pp. 1188–1193. ACM, New York (2007)Google Scholar
  6. 6.
    Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Specify, compile, run: Hardware from PSL. Electr. Notes Theor. Comput. Sci. 190(4), 3–16 (2007)CrossRefGoogle Scholar
  7. 7.
    Bloem, R., Greimel, K., Henzinger, T.A., Jobstmann, B.: Synthesizing robust systems. In: FMCAD, pp. 85–92. IEEE, Los Alamitos (2009)Google Scholar
  8. 8.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35(8), 677–691 (1986)CrossRefzbMATHGoogle Scholar
  9. 9.
    Chatterjee, K., Henzinger, T.A., Horn, F.: Finitary winning in omega-regular games. ACM Trans. Comput. Log. 11(1) (2009)Google Scholar
  10. 10.
    de Alfaro, L., Faella, M.: An accelerated algorithm for 3-color parity games with an application to timed games. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 108–120. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Dimitrova, R., Finkbeiner, B.: Synthesis of Fault-Tolerant Distributed Systems. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 321–336. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Ehlers, R.: Symbolic bounded synthesis. In: [24], pp. 365–379Google Scholar
  13. 13.
    Ehlers, R.: Generalised Rabin(1) synthesis. arXiv/CoRR abs/1003.1684 (2010)Google Scholar
  14. 14.
    Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS, pp. 368–377. IEEE, Los Alamitos (1991)Google Scholar
  15. 15.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games: A Guide to Current Research. LNCS, vol. 2500. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  16. 16.
    Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theor. Comput. Sci. 363(2), 182–195 (2006)CrossRefzbMATHGoogle Scholar
  17. 17.
    Kress-Gazit, H., Fainekos, G.E., Pappas, G.J.: Temporal-logic-based reactive mission and motion planning. IEEE Transactions on Robotics 25(6), 1370–1381 (2009)CrossRefGoogle Scholar
  18. 18.
    Krishnan, S.C., Puri, A., Brayton, R.K., Varaiya, P.: The Rabin index and chain automata, with applications to automatas and games. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 253–266. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  19. 19.
    McNaughton, R.: Infinite games played on finite graphs. Ann. Pure Appl. Logic 65(2), 149–184 (1993)CrossRefzbMATHGoogle Scholar
  20. 20.
    Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, Weizmann Institute of Science, Rehovot, Israel (March 1989)Google Scholar
  22. 22.
    Thomas, W.: Automata on Infinite Objects. In: Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 133–191. MIT Press, Cambridge (1994)Google Scholar
  23. 23.
    Thomas, W.: Church’s problem and a tour through automata theory. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 635–655. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  24. 24.
    Touili, T., Cook, B., Jackson, P. (eds.): CAV 2010. LNCS, vol. 6174. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  25. 25.
    Wongpiromsarn, T., Topcu, U., Murray, R.M.: Automatic synthesis of robust embedded control software. In: AAAI Spring Symposium on Embedded Reasoning (2010)Google Scholar
  26. 26.
    Wongpiromsarn, T., Topcu, U., Murray, R.M.: Receding horizon control for temporal logic specifications. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 101–110. ACM, New York (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rüdiger Ehlers
    • 1
  1. 1.Reactive Systems GroupSaarland UniversityGermany

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