Logic of Programs 1985: Logics of Programs pp 196-218 | Cite as

The glory of the past

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 193)


An extension of propositional temporal logic that includes operators referring to a bounded past is considered. An exponential time decision procedure and a complete axiomatic system are presented. A suggested normal form leads to a syntactic classification of safety and liveness formulae. The adequacy of temporal logic to modular verification is examined. Finally we present the notion of α-fairness which is proved to fully capture the behavior of probabilistic finite state programs.


Temporal Logic Deductive System Past Operator Computation Tree Concurrent Program 
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  1. [AS]
    Alpern, B., Schneider, F.B., — Defining Liveness, Cornell University, (Oct. 1984).Google Scholar
  2. [BK]
    Barringer, H., Kuiper R., — A Temporal Logic Specification Method Supporting Hierarchical Development, University of Manchester, (Nov. 1983).Google Scholar
  3. [BKP]
    Barringer, H., Kuiper, R., Pnueli, A. — Now You May Compose Temporal Logic Specifications, 16th Symposium on Theory of Computing (April 84), 51–63.Google Scholar
  4. [Buc]
    Büchi, J.R., — On a Decision Method in Restricted Second Order Arithmetic, Proc. Intern. Congr. Logic, and Philos. Sci. 1960, 1960, Stanford University Press (1962) 1–11.Google Scholar
  5. [Buc]
    Büchi, J.R., — Weak Second Order Arithmetics and Finite Automata, Z. Math. Logik Grundlagen Math 6 (1960) 66–92.Google Scholar
  6. [Bur]
    Burgess, J., — Basic Tense Logic, in Handbook of Philosophical Logic, Vol. 2 (D. Gabbay and F. Guenthner eds.) D. Reidel Pub. Co., (1984).Google Scholar
  7. [C]
    Choueka, Y., — Theories of Automata on ω-Tapes: A Simplified Approach, Journal of Computers and Systems Sciences 8 (1974) 117–141.Google Scholar
  8. [CH]
    Chen, Z.C., Hoare, C.A.R., — Partial Correctness of Communicating Processes and Protocols, Technical Monograph, PRG-20 Oxford University Computing Laboratory (May 1981).Google Scholar
  9. [GPSS]
    Gabbay, D., Pnueli, A., Shelah, S., Stavi, J., — On the Temporal Analysis of Fairness, Proc of the 7th ACM Symp. on Principles of Programming Languages (1980) 163–173.Google Scholar
  10. [H]
    Hoare, C.A.R., — A Calculus of Total Correctness for Communicating Precesses, Technical Monograph, RPG-23 Oxford University Computing Laboratory (May 1981).Google Scholar
  11. [HO]
    Hailpern, B., Owicki, S., — Modular Verification of Computer Communication Protocols, IEEE Trans. on Communications, COM-31, 1 (Jan. 1983) 56–68.Google Scholar
  12. [K]
    Kamp, H.W., — Tense Logic and the Theory of Linear Order, Ph.D. Thesis, University of California Los Angeles (1968).Google Scholar
  13. [KVR]
    Koymans, R., Vytopil, J., DeRoever, W.P., — Real Time Programming and Asynchronous Message Passing, 2nd ACM Symp. of Distributed Computing, Montreal (1983) 187–197.Google Scholar
  14. [L]
    Lamport, L., — What is Good in Temporal Logic?, Proceeding IFIP (1983) 657–668.Google Scholar
  15. [Li]
    Lichtenstein, O., — Decidability and Completeness of a Temporal Proof System for Finite State Programs, M.Sc. Thesis, Tel Aviv University (1984).Google Scholar
  16. [LP]
    Lichtenstein, O., Pnueli, A., — Checking That Finite State Concurrent Programs Satisfy Their Linear Specification, ACM Symp. on Principles of Programming Languages (1985).Google Scholar
  17. [MC]
    Misra, J., Chandy, K.M., — Proofs of Networks of Processes, IEEE Trans. on Software Engineering 5E-7, 4 (July 1981).Google Scholar
  18. [MNP]
    McNaughton, R., Papert, S., — Counter Free Automata, MIT press, Cambridge, Mass (1971).Google Scholar
  19. [MP1]
    Manna, Z., Pnueli, A., — Verification of Concurrent Programs: A Temporal Proof System, Proc. 4th School on Advanced Programming, Amsterdam (June 1982) 163–255.Google Scholar
  20. [MP2]
    Manna, Z., Pnueli, A., — How to Cook a Temporal Proof System for your Pet Programming Language Proc of the 10th ACM Symp. on Principles of Programming Languages (1983).Google Scholar
  21. [MP3]
    Manna, Z., Pnueli, A., — Adequate Proof Principles for Invariance and Liveness Properties of Concurrent Programs, Science and Computer Programming, Forthcoming.Google Scholar
  22. [NGO]
    Nguyen, V., Gries, D., Owicki, S., — A Model and Temporal Proof System for Networks of Processes, Proc of the 12th ACM Symp. on Principles of Programming Languages (1985).Google Scholar
  23. [OG]
    Owicki, S., Gries, D., — An axiomatic Proof Technique for Parallel Programs, Acta Informatica 6 (1976) 319–340.Google Scholar
  24. [OL]
    Owicki, S., Lamport, L., — Proving Liveness Properties of Concurrent Programs, ACM TOPLAS 4,3 (July 1982) 455–495.Google Scholar
  25. [Pe]
    Peikert, R., — Propositional Temporal Logic and ω-regular Languages, Manuscript, ETH-Zürich.Google Scholar
  26. [Pn1]
    Pnueli, A., — The Temporal Logic of Programs, 18th Annual Symp. on Foundation of Computer Science (1977) 46–57.Google Scholar
  27. [Pn2]
    Pnueli, A., — In Transition from Global to Modular Temporal Reasoning about Programs, Proc. Advanced NATO Institute on Logic and Models for Verification and Specification of Concurrent Systems, La Colle-Sur-Loupe (Oct. 1984).Google Scholar
  28. [Pn3]
    Pnueli, A., — On the Extremely Fair Treatment of Probabilistic Algorithms, Proc. of the 15th Annual ACM Symp. on Theory of Computing (1983).Google Scholar
  29. [Pr]
    Prior, — Past Present and Future, Oxford Press.Google Scholar
  30. [RU]
    Rescher, N., Urquhart, A., — Temporal Logic, Springer Verlag (1971).Google Scholar
  31. [S]
    Sistla, A.P., — Characterization of Safety and Liveness Properties in Temporal Logic, University of Massachusetts, Amherst (Nov. 1984).Google Scholar
  32. [SC]
    A.P. Sistla, E.M. Carke, The Complexity of Propositional Temporal Logic, 14th ACM Symposium on Thoery of Computing, (May 1982) 159–167.Google Scholar
  33. [T]
    Thomas, W., — A Combinatorial Approach to the Theory of ω-Automata, Information and Control 48,3 (March 1981) 261–283.Google Scholar
  34. [VW]
    Vardi, M.Y., Wolper, P., — Expressiveness and Complexity of Languages for Describing Sequences, Stanford University.Google Scholar
  35. [W]
    Wolper, P., — Temporal Logic can be More Expressive, Proc. of the 22nd Annual Symp. on Foundation of Computer Science (1981) 340–348.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  1. 1.Dept. of Computer ScienceTel Aviv UniversityIsrael
  2. 2.Dept. of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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