Advertisement

Acta Informatica

, Volume 20, Issue 3, pp 207–226 | Cite as

The temporal logic of branching time

  • Mordechai Ben-Ari
  • Amir Pnueli
  • Zohar Manna
Article

Summary

A temporal logic is defined which contains both linear and branching operators. The underlying model is the tree of all possible computations. The following metatheoretical results are proven: 1) an exponential decision procedure for satisfiability; 2) a finite model property; 3) the completeness of an axiomatization.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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.
    Abrahamson, K.R.: Modal logic of concurrent nondeterministic programs. Symposium on Semantics of Concurrent Computations, Lecture Notes in Computer Science 70, pp. 21–33. Berlin, Heidelberg, New York: Springer 1979Google Scholar
  2. 2.
    Ben-Ari, M., Manna, Z., Pnueli, A.: The temporal logic of branching time. Eight ACM Symposium on Principles of Programming Languages, Williamsburg, VA, pp. 164–176, 1981Google Scholar
  3. 3.
    Emerson, A.E., Halpern, J.Y.: Decision procedures and expressiveness in the temporal logic of branching time. 14-th ACM Symposium on Theory of Computing, San Francisco, CA, pp. 169–180, 1982Google Scholar
  4. 4.
    Floyd, R.W.: Nondeterministic algorithms. J. ACM14(4), 636–644 (1967)Google Scholar
  5. 5.
    Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: The temporal analysis of fairness. Seventh ACM Symposium on Principles of Programming Languages, Las Vegas, NE, pp. 163–173, 1980Google Scholar
  6. 6.
    Harel, D.: First Order Dynamic Logic, Lecture Notes in Computer Science 68. Berlin, Heidelberg, New York: Springer 1979Google Scholar
  7. 7.
    Harel, D., Kozen, D., Parikh, R.: Process Logic: expressiveness, decidability, completeness. 21-st IEEE Symposium on Foundation of Computer Science, pp. 129–142, 1980Google Scholar
  8. 8.
    Kröger, A.: A uniform logical basis for the description, specification and verification of programs. IFIP Working Conference on Formal Description of Programming Concepts, St. Andrews, Canada, 1977Google Scholar
  9. 9.
    Lamport, L.: “Sometime” is sometimes “not never”. Seventh ACM Symposium on Principles of Programming Languages, Las Vegas, NE, pp. 174–183, 1980Google Scholar
  10. 10.
    Manna, Z.: Second order mathematical theory of computation. Second ACM Symposium on Theory of Computing, pp. 158–168, 1970Google Scholar
  11. 11.
    Manna, Z., Pnueli, A.: The modal logic of programs. Automata, Languages and Programming, Lecture Notes in Computer Science 79, pp. 385–409. Berlin, Heidelberg, New York: Springer 1979Google Scholar
  12. 12.
    Pnueli, A.: The temporal semantics of concurrent programs. Theor. Comput. Sci.13, 45–60 (1981)Google Scholar
  13. 13.
    Pratt, V.R.: A near optimal method for reasoning about action. J. Comput. Syst. Sci.20, 231–254 (1980)Google Scholar
  14. 14.
    Prior, A.: Past, Present and Future. Oxford University Press 1967Google Scholar
  15. 15.
    Rescher, N., Urquhart, A.: Temporal Logic. Berlin, Heidelberg, New York, Wien: Springer 1971Google Scholar
  16. 16.
    Smullyan, R.M.: First Order Logic. Berlin, Heidelberg, New York: Springer 1968Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Mordechai Ben-Ari
    • 1
  • Amir Pnueli
    • 2
  • Zohar Manna
    • 2
    • 3
  1. 1.Department of Computer ScienceSchool of Mathematical Sciences, Tel Aviv UniversityTel AvivIsrael
  2. 2.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  3. 3.Department of Computer ScienceStanford UniversityStanfordUSA

Personalised recommendations