Temporal verification diagrams

  • Zohar Manna
  • Amir Pnueli
Invited Talk 7
Part of the Lecture Notes in Computer Science book series (LNCS, volume 789)


Most formal approaches to the verification of temporal properties of reactive programs infer temporal conclusions from verification conditions that are state formulas, i.e., contain no temporal operators. These proofs can often be effectively presented by the use of verification diagrams. In this paper, we present a self-contained presentation of verification diagrams for proving various temporal properties.

Beginning with safety properties, we present WAIT-POR and INVARIANCE diagrams for proving wait-for (precedence) and invariance formulas. Proceeding to liveness properties, we present verification diagrams for response properties that require a bounded number of helpful steps (CHAIN diagrams) and response properties that require an unbounded number of helpful steps (RANK diagrams).

Additional types of diagrams are proposed for handling response properties for parameterized programs (e.g., P-RANK diagrams) and response properties that rely on the full spectrum of fairness requirements, including compassionate helpful transitions (e.g., F-CHAIN diagrams).


verification diagrams temporal logic reactive systems formal verification 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AS89]
    B. Alpern and F.B. Schneider. Verifying temporal properties without temporal logic. ACM Trans. Prog. Lang. Sys., 11:147–167, 1989.Google Scholar
  2. [Har87]
    D. Harel. Statecharts: A visual formalism for complex systems. Sci. Comp. Prog., 8:231–274, 1987.Google Scholar
  3. [HO83]
    B.T. Hailpern and S.S. Owicki. Modular verification of computer commuincation protocols. IEEE Trans. on Commun., COM-31(1):56–68, 1983.Google Scholar
  4. [Lam91]
    L. Lamport. The temporal logic of actions. Technical report, Digital Equipment Corporation, Systems Research Center, 1991.Google Scholar
  5. [MP83]
    Z. Manna and A. Pnueli. Verification of concurrent programs: A temporal proof system. In J.W. de Bakker and J. Van Leeuwen, editors, Foundations of Computer Science IV, Distributed Systems: Part 2, pages 163–255. Mathematical Centre Tracts 159, Center for Mathematics and Computer Science (CWI), Amsterdam, 1983.Google Scholar
  6. [MP84]
    Z. Manna and A. Pnueli. Adequate proof principles for invariance and liveness properties of concurrent programs. Sci. Comp. Prog., 32:257–289, 1984.Google Scholar
  7. [MP91a]
    Z. Manna and A. Pnueli. Completing the temporal picture. Theor. Comp. Sci., 83(1):97–130, 1991.Google Scholar
  8. [MP91b]
    Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, New York, 1991.Google Scholar
  9. [MP93]
    Z. Manna and A. Pnueli. Models for reactivity. Acta Informatica, 30:609–678, 1993.Google Scholar
  10. [MP94]
    Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems. Springer-Verlag, New York, 1994. To Appear.Google Scholar
  11. [NGO85]
    V. Nguyen, D. Gries, and S. Owicki. A model and temporal proof system for network of processes. In Proc. 12th ACM Symp. Princ. of Prog. Lang., pages 121–131, 1985.Google Scholar
  12. [OL82]
    S. Owicki and L. Lamport. Proving liveness properties of concurrent programs. ACM Trans. Prog. Lang. Sys., 4:455–495, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Zohar Manna
    • 1
  • Amir Pnueli
    • 2
  1. 1.Department of Computer ScienceStanford UniversityStanford
  2. 2.Department of Applied Mathematics and Computer ScienceWeizmann InstituteRehovotIsrael

Personalised recommendations