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Synthesis of Distributed Systems from Knowledge-Based Specifications

  • Ron van der Meyden
  • Thomas Wilke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)

Abstract

We consider the problem of synthesizing protocols in a distributed setting satisfying specifications phrased in the logic of linear time and knowledge. On the one hand, we show that synthesis is already undecidable in environments with just two agents, one of which observes every aspect of the system state and one of which observes nothing of it. This falsifies a conjecture of van der Meyden and Vardi from CONCUR’96. On the other hand, we prove that synthesis is decidable in broadcast environments, verifying a conjecture of van der Meyden and Vardi from the same paper, and we show that for specifications that are positive in the knowledge modalities the synthesis problem can be reduced to the same problem for formulas without knowledge modalities. After adapting Pnueli and Rosner’s decidability result on synthesis for linear temporal logic specifications in hierarchical environments, we obtain that, in our setting, synthesis is decidable for specifications positive in the knowledge modalities when restricted to hierarchical environments. We conclude the decidability in hierarchical systems of a property closely related to nondeducibility on strategies, a notion that has been studied in computer security.

Keywords

Linear Time Temporal Logic Linear Temporal Logic Hierarchical System Synthesis Problem 
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.
    Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controlers with partial observation. Theoretical Computer Science 303(1), 7–34 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Attie, P.C., Arora, A., Emerson, E.A.: Synthesis of fault-tolerant concurrent programs. ACM Transactions on Programming Languages and Systems 26(1), 125–1851 (2004)CrossRefGoogle Scholar
  3. 3.
    Chaum, D.: The dining cryptographers problem: unconditional sender and recipient untraceability. J., Cryptology (1), 65–75 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Emerson, E.A., Clarke, E.M.: Using branching time logic to synthesize synchronization skeletons. Science of Computer Programming 2, 241–266 (1982)zbMATHCrossRefGoogle Scholar
  5. 5.
    Engelhardt, K., van der Meyden, R., Su, K.: Modal logics with a hierarchy of local propositional quantifiers. In: Balbiani, P., Suzuki, N., Wolter, F., Zakharyaschev, M. (eds.) Advances in Modal Logic, vol. 4, pp. 9–30. World Scientific, Singapore (2003)Google Scholar
  6. 6.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  7. 7.
    Halpern, J.Y., O’Neill, K.: Anonymity and information hiding in multiagent systems. In: Proceedings of the 16th IEEE Computer Security Foundations Workshop, pp. 75–88 (2003)Google Scholar
  8. 8.
    Kupferman, O., Vardi, M.Y.: Synthesis with incomplete informatio. In: 2nd International Conference on Temporal Logic, Manchester, pp. 91–106 (July 1997)Google Scholar
  9. 9.
    Madhusudan, P.: Control and Synthesis of Open Reactive Systems. PhD thesis, University of Madras (November 2001) Google Scholar
  10. 10.
    Manna, Z., Wolper, P.: Synthesis of communicating processes from temporal logic specifications. ACM Transactions on Programming Languages and Systems 6(1), 68–93 (1984)zbMATHCrossRefGoogle Scholar
  11. 11.
    Mayr, R.: Undecidable problems in unreliable computations. Theoretical Computer Science 297(1-3), 337–354 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    van der Meyden, R.: Finite state implementations of knowledge-based programs. In: Chandru, V., Vinay, V. (eds.) FSTTCS 1996. LNCS, vol. 1180, pp. 262–273. Springer, Heidelberg (1996)Google Scholar
  13. 13.
    van der Meyden, R., Su, K.: Symbolic model checking the knowledge of the dining cryptographers. In: Proc. 17th IEEE Computer Security Foundations Workshop, pp. 280–291 (June 2004)Google Scholar
  14. 14.
    van der Meyden, R., Vardi, M.Y.: Synthesis from knowledge-based specifications. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 34–49. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. 16th ACM Symp. on Principles of Programming Languages, Austin (January 1989)Google Scholar
  16. 16.
    Pnueli, A., Rosner, R.: On the synthesis of an asynchronous reactive module. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 652–671. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  17. 17.
    Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: Proc. 31st IEEE Symp. on Foundation of Computer Science, pp. 746–757 (1990)Google Scholar
  18. 18.
    Vardi, M.Y.: An automata-theoretic approach to fair realizability and synthesis. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 267–292. Springer, Heidelberg (1995)Google Scholar
  19. 19.
    Walukiewicz, I.: A landscape with games in the background. In: Proc. IEEE Symp. on Logic In computer Science, pp. 356–366 (2004)Google Scholar
  20. 20.
    Wittbold, J.T., Johnson, D.M.: Information flow in nondeterministic systems. In: Proc. IEEE Symp. on Research in Security and Privacy, pp. 144–161 (1990)Google Scholar
  21. 21.
    Wong-Toi, H., Dill, D.L.: Synthesizing processes and schedulers from temporal specifications. In: Clarke, E.M., Kurshan, R.P. (eds.) Computer-Aided Verification 1990, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 3, pp. 177–186. AMS (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ron van der Meyden
    • 1
  • Thomas Wilke
    • 2
  1. 1.School of Computer Science and EngineeringUniversity of New South Wales & National ICTAustralia
  2. 2.Institut für InformatikChristian-Albrechts-Universität zu Kiel 

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