Advertisement

Lazy Semiring Neighbours and Some Applications

  • Peter Höfner
  • Bernhard Möller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)

Abstract

We extend an earlier algebraic approach to Neighbourhood Logic (NL) from domain semirings to lazy semi-rings yielding lazy semiring neighbours. Furthermore we show three important applications for these. The first one extends NL to intervals with infinite length. The second one applies lazy semiring neighbours in an algebraic semantics of the branching time temporal logic CTL *. The third one sets up a connection between hybrid systems and lazy semiring neighbours.

Keywords

Hybrid System Boolean Algebra Temporal Logic Great Element Galois Connection 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Conway, J.H.: Regular Algebra and Finite State Machines. Chapman and Hall, Boca Raton (1971)Google Scholar
  2. 2.
    Desharnais, J., Möller, B., Struth, G.: Kleene Algebra with Domain. ACM Trans. Computational Logic (to appear 2006); Preliminary version: Universität Augsburg, Institut für Informatik, Report No. 2003-07 (June 2003)Google Scholar
  3. 3.
    Dutertre, B.: Complete Proof Systems for First-Order Interval Temporal Logic. In: Proc. 10th Annual IEEE Symb. on Logic in Computer Science, pp. 36–43. IEEE Press, Los Alamitos (1995)CrossRefGoogle Scholar
  4. 4.
    Emerson, E.A.: Temporal and Modal Logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 995–1072. Elsevier, Amsterdam (1991)Google Scholar
  5. 5.
    Halpern, J.Y., Moszkowski, B., Manna, Z.: A Hardware Semantics Based on Temporal Intervals. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 278–291. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  6. 6.
    Halpern, J.Y., Shoham, Y.: A Propositional Modal Logic of Time Intervals. In: Proceedings of the First IEEE Symposium on Logic in Computer Science, pp. 279–292. IEEE Press, PiscatawayGoogle Scholar
  7. 7.
    Höfner, P.: Semiring Neighbours — An Algebraic Embedding and Extension of Neighbourhood Logic. In: van de Pol, J., Romijn, J., Smith, G. (eds.): IFM 2005 Doctoral Symposium on Integrated Formal Methods, 6–13 (2005) Extended version: P. Höfner: Semiring Neighbours. Technical Report 2005-19, Universität Augsburg (2005)Google Scholar
  8. 8.
    Höfner, P., Möller, B.: Towards an Algebra of Hybrid Systems. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929, pp. 121–133. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Kozen, D.: Kleene Algebra with Tests. ACM Trans. Programming Languages and Systems 19(3), 427–443 (1997)CrossRefGoogle Scholar
  10. 10.
    Möller, B.: Kleene Getting Lazy. Science of Computer Programming. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 252–273. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Möller, B., Höfner, P., Struth, G.: Quantales and Temporal Logics. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 263–277. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Sintzoff, M.: Iterative Synthesis of Control Guards Ensuring Invariance and Inevitability in Discrete-Decision Games. In: Owe, O., Krogdahl, S., Lyche, T. (eds.) From Object-Orientation to Formal Methods. LNCS, vol. 2635, pp. 272–301. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Venema, Y.: A Modal Logic for Chopping Intervals. J. of Logic and Computation 1(4), 453–476 (1990)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Zhou, C., Hansen, M.R.: An Adequate First Order Interval Logic. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 584–608. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Zhou, C., Hansen, M.R.: Duration Calculus – A Formal Approach to Real-Time Systems. Monographs in Theoretical Computer Science. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  16. 16.
    Zhou, C., Van Hung, D., Xiaoshan, L.: Duration Calculus with Infinite Intervals. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 16–41. Springer, Heidelberg (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Höfner
    • 1
  • Bernhard Möller
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany

Personalised recommendations