Skip to main content
SpringerLink
Log in
Book cover

Workshop/School/Symposium of the REX Project (Research and Education in Concurrent Systems)

REX 1991: Real-Time: Theory in Practice pp 176–194Cite as

Real-time and the Mu-Calculus (preliminary report)

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 600))

Abstract

We argue that the Mu-Calculus provides a conceptually advantageous framework for specifying and reasoning about Real-Time Systems. We show that mechanical reasoning can be done efficiently in a quantitative formulation of the Mu-Calculus. Our work also suggests a new complexity theory for reactive systems.

This work was supported in part by NSF grant DCR-8511354 and ONR Contract N00014-89-J-1913.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abrahamson, K. Decidability and Expressiveness of Logics of Processes, Ph.D. Thesis, Univ. of Washington, 1980.

    Google Scholar 

  2. Alur, R., Techniques for Automatic Verification of Real-Time Systems, PhD Thesis, Computer Science Department, Stanford University, August 1991, Technical Report STAN-CS-91-1378.

    Google Scholar 

  3. Alur, R., Courcoubetis, C, and Dill, D., Model-checking for Real-Time Systems, Proc. of the Fifth IEEE Symp. on Logic in Computer Science (LICS), pp. 414–425, 1990.

    Google Scholar 

  4. Arnold, A., and Crubille, P., A Linear Time Algorithm to Solve Fixed Point Equations of Transitions Systems, Information Processing Letters, vol. 29, pp. 57–66, Sept., 1988.

    Article  Google Scholar 

  5. Browne, M.C., An Improved Algorithm for the Automatic Verification of Finite State Systems Using Temporal Logic, Proc. Symp. on Logic in Computer Science, Cambridge, pp. 260–266, 1986.

    Google Scholar 

  6. Burgess, J., Basic Tense Logic, in Handbook of Philosophical Logic, D. Gabbay and F. Guenthner, eds., D. Reidel Pub. Co, 1984.

    Google Scholar 

  7. Chandra, A., Kozen, D., and Stockmeyer, L., Alternation, JACM, vol. 28, no. 1, pp. 114–133, 1981.

    Article  Google Scholar 

  8. Clarke, E.M., E.A. Emerson, Design and Synthesis of Synchronization Skeletons Using Branching Time Temporal Logic, Proc. of the Workshop on Logics of Programs, Yorktown Heights, D. Kozen, editor, LNCS#131, Springer-Verlag, pp. 52–71, 1981.

    Google Scholar 

  9. Clarke, E.M., E.A. Emerson, A.P. Sistla, Automatic Verification of Finite State Concurrent Systems Using Temporal Logic Specifications: A Practical Approach, Proc. 10th Annual ACM Symp. on Principles of Programming Languages, Austin, pp. 117–126, 1983; also appeared in ACM Transactions on Programming Languages and Systems, vol. 8, no. 2, pp. 244–263, 1986.

    Google Scholar 

  10. Clarke, E., and Grumber, O., Research on Automatic Verification of Finite State Concurrent Systems, Ann. Rev. Comp. Sci., vol. 2, pp. 269–290, 1987.

    Article  Google Scholar 

  11. E. Clarke, S. Bose, M. Browne, O. Grumberg, The Design and Verification of Finite State Hardware Controllers, Technical Report CMU-CS-87-145, Carnegie-Mellon Univ., July 1987.

    Google Scholar 

  12. Cleaveland, R., and Steffen, B., A Linear Time Model Checking Algorithm for the Alternation Free Modal Mu-Calculus, Proc. of the Third Workshop on Computer Aided Verification (Participant's Version), ed. K. Larsen and A. Skou, Math. and CS Dept, Univ. of Aalbourg, Denmark, July 1–4, 1991.

    Google Scholar 

  13. de Bakker, J. W., Mathematical Theory of Program Correctness, Prentice-Hall, Englewood Cliffs, NJ, 1980.

    Google Scholar 

  14. de Roever, W.P., Recursive Program Schemes: Semantics and Proof Theory, Mathematical Centre Tracts 70, Mathematisch Centrum, Amsterdam, 1976.

    Google Scholar 

  15. de Roever, W.-P., editor, Real-Time: Theory in Practice, Springer LNCS, to appear.

    Google Scholar 

  16. Dijkstra, E.W., A Discipline of Programming, Prentice-Hall, 1976.

    Google Scholar 

  17. Emerson, E.A., Temporal and Modal Logic, in Handbook of Theoretical Computer Science, vol. B., J. van Leeuwen, editor, North-Holland, pp. 995–1072

    Google Scholar 

  18. Emerson, E.A., E.M. Clarke, Characterizing Correctness Properties of Parallel Programs Using Fixpoints, Proc. 7th Annual International Colloquium on Automata, Languages and Programming, LNCS#85, Springer-Verlag, pp. 169–181, 1980.

    Google Scholar 

  19. Emerson, E.A., E.M. Clarke, Using Branching Time Logic to Synthesize Synchronization Skeletons, Science of Computer Programming, vol. 2, pp. 241–266, 1982.

    Article  Google Scholar 

  20. Emerson, E.A., J.Y. Halpern, Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. of the 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 169–180, 1982; also appeared in Journal of Computer and System Sciences, vol 30, no. 1, pp. 1–24, 1985.

    Google Scholar 

  21. Emerson, E.A., C.L. Lei, Modalities for Model Checking: Branching Time Logic Strikes Back, Proc. 12th Annual ACM Symp. on Principles of Programming Languages, New Orleans, pp. 84–96, 1985; also appeared in Science of Computer Programming, vol. 8, pp. 275–306, 1987.

    Google Scholar 

  22. Emerson, E. A., and Lei, C.-L., Efficient Model Checking in Fragments of the Mu-Calculus, IEEE Symp. on Logic in Computer Science, 1986.

    Google Scholar 

  23. Emerson, E.A., C.L. Lei, New Results on Model-Checking in the Prepositional Mu-Calculus, presented at the Colloquium on Temporal Logic and Specification, Altrincham, England, 1987.

    Google Scholar 

  24. Emerson, E. A., Mok, A. K., Sistla, A. P., and Srinivasan, J., Quantitative Temporal Reasoning, Proceedings of the Workshop on Automatic Verification Methods for Finite State Systems (Participants Version), C-cube, the French National Concurrency Project, June 12–14, 1989.

    Google Scholar 

  25. Fischer, M., and Ladner, R., Propositional Dynamic Logic of Regular Programs, JCSS, vol. 18, no. 2, pp. 194–211, 1979.

    Google Scholar 

  26. Gerth, R., and Boucher, A., A Timed Failures Model for Extending Communicating Processes, In Proc. of the 14th Ann. ICALP, pp. 95–114, Springer LNCS no. 267, 1987.

    Google Scholar 

  27. Henzinger, T., The Temporal Specification and Verification of Real Time Systems, PhD Thesis, Computer Science Department, Stanford University, August 1991, Technical Report STAN-CS-91-1380.

    Google Scholar 

  28. Hooman, J. Specification and Compositional Verification of Real Time Systems, PhD Thesis, Eindhoven University of Technology, 1991.

    Google Scholar 

  29. Jahanian, F., and A. K. Mok, Safety Analysis of Timing Properties in Real Time Systems, IEEE Trans. Software Eng., SE-12(9), pp. 890–904, 1986.

    Google Scholar 

  30. Jahanian, F., A.K. Mok, A Graph-Theoretic Approach for Timing Analysis and its Implementation, IEEE Transactions on Computers, vol. C-36, no. 8, pp. 961–975, 1987.

    Google Scholar 

  31. Jahanian, F., and Mok, A., A Method for Verifying Properties of Modechart Specifications, Proc. of the Ninth IEEE Real-Time Systems Symposium, pp. 12–21, 1988.

    Google Scholar 

  32. Koymans, R., Specifying Message Passing and Time Critical Systems with Temporal Logic, PhD Thesis, Eindhoven University of Technology, 1989.

    Google Scholar 

  33. Koymans, R. Specifying Real Time Properties with Metric Temporal Logic, Real Time Systems, vol. 2, no. 4., pp. 255–299, 1990.

    Article  Google Scholar 

  34. Koymans, R., Vytopil, J., and de Roever, W.-P., Real Time Programming and Asynchronous Message Passing, Proceedings of the Second Annual ACM Symp. on Principles of Distributed Computing (PODC), pp. 187–197, 1983.

    Google Scholar 

  35. Kozen, D., Results on the Propositional μ-Calculus, Proc. 9th Annual International Colloquium on Automata, Languages and Programming, LNCS#140, Springer-Verlag, pp. 348–359, 1982; also appeared in Theoretical Computer Science, vol. 27, no. 3, pp. 333–354, 1983.

    Google Scholar 

  36. Lewis, H. R., A Logic of Concrete Time Intervals, Proceedings of the Fifth Annual Symposium on Logic in Computer Science (LICS), IEEE Press, pp. 380–399, 1990.

    Google Scholar 

  37. Lichtenstein, O., A. Pnueli, Checking That Finite State Concurrent Programs Satisfy Their Linear Specification, Proc. 12th Annual ACM Symp. on Principles of Programming Languages, New Orleans, pp. 97–107, 1985.

    Google Scholar 

  38. Lichtenstein, O., A. Pnueli, L. Zuck, The Glory of The Past, Proc. Conf. on Logics of Programs, Brooklyn, R. Parikh, editor, LNCS#193, Springer-Verlag, pp. 196–218,1985.

    Google Scholar 

  39. Manna., Z., P. Wolper, Synthesis of Communicating Processes from Temporal Logic Specifications, ACM Transactions on Programming Languages and Systems, vol. 6, no. 1, pp. 68–93, 1984.

    Article  Google Scholar 

  40. Ostroff, J., Temporal Logic of Real-Time Systems, Research Studies Press, 1990.

    Google Scholar 

  41. Pnueli, A., The Temporal Logic of Programs, 18th Annual Symp. on Foundations of Computer Science, Providence, pp. 46–57,1977.

    Google Scholar 

  42. Pnueli, A., and Harel, E., Application of Temporal Logic to the Specification of Real-Time Systems, in Formal Techniques in Real-Time and Fault Tolerant Systems, M. Joseph (ed.), Springer LNCS #331, 1988.

    Google Scholar 

  43. Pnueli, A., R. Rosner, On the Synthesis of a Reactive Module, Proc. 16th Annual ACM Symp. on Principles of Programming Languages, Austin, pp. 179–190, 1989.

    Google Scholar 

  44. Queille, J.P., J. Sifakis, Specification and Verification of Concurrent Systems in CESAR, Proc. of the 5th International Symposium on Programming, LNCS#137, Springer-Verlag, pp. 337–350, 1981.

    Google Scholar 

  45. Pratt, V., A Decidable Mu-Calculus, 22nd FOCS, pp. 421–427, 1981.

    Google Scholar 

  46. Scott, D., and de Bakker, J., A Theory of Programs, unpublished notes, IBM seminar, Vienna, 1969.

    Google Scholar 

  47. Sistla, A.P., E.M. Clarke, The Complexity of Prepositional Linear Temporal Logics, Proc. of the 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 159–168, 1982; also appeared in Journal ACM, vol. 32, no. 3, pp. 733–749, 1985.

    Google Scholar 

  48. Streett, R., Emerson, E. A., An Automata-Theoretic Decision Procedure for the Propositional Mu-calculus, ICALP84, also appears in Information and Computation, vol. 81, no. 3, June 1989., pp. 249–264.

    Article  Google Scholar 

  49. van Benthem, J., The Logic of Time, D. Reidel Pub. Co., 1983.

    Google Scholar 

  50. Wolper, P., Temporal Logic can be More Expressive, Information and Control, 1983.

    Google Scholar 

  51. Yodaiken, V., and Ramamritham, K., Specifying and Verifiying a Real-Time Priority Queue with Modal Algebra, Proc. 11th IEEE Symp on Real-Time Systems, pp. 300–311, Dec. 5–7, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Texas at Austin, 78712, Austin, Texas, USA

    E. Allen Emerson

Authors
  1. E. Allen Emerson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. W. de Bakker C. Huizing W. P. de Roever G. Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Emerson, E.A. (1992). Real-time and the Mu-Calculus (preliminary report). In: de Bakker, J.W., Huizing, C., de Roever, W.P., Rozenberg, G. (eds) Real-Time: Theory in Practice. REX 1991. Lecture Notes in Computer Science, vol 600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031992

Download citation

  • DOI: https://doi.org/10.1007/BFb0031992

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55564-3

  • Online ISBN: 978-3-540-47218-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation