Complexity of Decision Problems for Mixed and Modal Specifications

  • Adam Antonik
  • Michael Huth
  • Kim G. Larsen
  • Ulrik Nyman
  • Andrzej Wąsowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)

Abstract

We consider decision problems for modal and mixed transition systems used as specifications: the common implementation problem (whether a set of specifications has a common implementation), the consistency problem (whether a single specification has an implementation), and the thorough refinement problem (whether all implementations of one specification are also implementations of another one). Common implementation and thorough refinement are shown to be PSPACE-hard for modal, and so also for mixed, specifications. Consistency is PSPACE-hard for mixed, while trivial for modal specifications. We also supply upper bounds suggesting strong links between these problems.

References

  1. 1.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  2. 2.
    Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, Springer, Heidelberg (1981)CrossRefGoogle Scholar
  3. 3.
    Larsen, K.G., Thomsen, B.: A modal process logic. In: Third Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 203–210. IEEE Computer Society, Los Alamitos (1988)Google Scholar
  4. 4.
    Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Dams, D.: Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis, Eindhoven University of Technology (July 1996)Google Scholar
  6. 6.
    Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Trans. Program. Lang. Syst. 19(2), 253–291 (1997)CrossRefGoogle Scholar
  7. 7.
    Larsen, K.G., Nyman, U., Wąsowski, A.: On modal refinement and consistency. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 105–119. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Hussain, A., Huth, M.: On model checking multiple hybrid views. Technical report, Department of Computer Science, University of Cyprus, TR-2004-6 (2004)Google Scholar
  9. 9.
    Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: Fifth Annual IEEE Symposium on Logics in Computer Science (LICS), Philadelphia, PA, USA, June 4–7, 1990, pp. 108–117 (1990)Google Scholar
  10. 10.
    Hussain, A., Huth, M.: Automata games for multiple-model checking. Electr. Notes Theor. Comput. Sci. 155, 401–421 (2006)CrossRefGoogle Scholar
  11. 11.
    Fischbein, D., Uchitel, S., Braberman, V.: A foundation for behavioural conformance in software product line architectures. In: ROSATEA 2006 Proceedings, pp. 39–48. ACM Press, New York (2006)CrossRefGoogle Scholar
  12. 12.
    Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)Google Scholar
  13. 13.
    Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994)CrossRefGoogle Scholar
  14. 14.
    Park, D.: Concurrency and automata on infinite sequences. In: Proceedings of the 5th GI-Conference on Theoretical Computer Science, pp. 167–183. Springer, London, UK (1981)Google Scholar
  15. 15.
    Hüttel, H.: Operational and denotational properties of modal process logic. Master’s thesis, Computer Science Department. Aalborg University (1988)Google Scholar
  16. 16.
    Xinxin, L.: Specification and Decomposition in Concurrency. PhD thesis, Department of Mathematics and Computer Science, Aalborg University (April 1992)Google Scholar
  17. 17.
    Schmidt, H., Fecher, H.: Comparing disjunctive modal transition systems with a one-selecting variant. Submitted for publication to JLAP (2007)Google Scholar
  18. 18.
    Huth, M.: Labelled transition systems as a Stone space. Logical Methods in Computer Science 1(1), 1–28 (2005)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)MATHGoogle Scholar
  20. 20.
    Jonsson, B., Larsen, K.G.: On the complexity of equation solving in process algebra. In: Abramsky, S., Maibaum, T.S.E. (eds.) TAPSOFT 1991. LNCS, vol. 493, pp. 381–396. Springer, Heidelberg (1991)Google Scholar
  21. 21.
    Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  22. 22.
    Franceschet, M., de Rijke, M.: Model checking hybrid logics (with an application to semistructured data). J. Applied Logic 4(3), 279–304 (2006)MATHCrossRefGoogle Scholar
  23. 23.
    Antonik, A.: MPhil/PhD transfer report. Imperial College London, United Kingdom (January 2007)Google Scholar
  24. 24.
    Bruns, G., Godefroid, P.: Generalized model checking: Reasoning about partial state spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 168–182. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  25. 25.
    Wilke, T.: Alternating tree automata, parity games, and modal μ-calculus. Bull. Soc. Math. Belg. 8(2) (May 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Adam Antonik
    • 1
  • Michael Huth
    • 1
  • Kim G. Larsen
    • 2
  • Ulrik Nyman
    • 2
  • Andrzej Wąsowski
    • 2
    • 3
  1. 1.Department of ComputingImperial College LondonUnited Kingdom
  2. 2.Department of Computer ScienceAalborg UniversityDenmark
  3. 3.IT University of CopenhagenDenmark

Personalised recommendations