Advertisement

Predicates, temporal logic, and simulations

  • Ching-Tsun Chou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 780)

Abstract

We present an integrated theory of predicates, temporal logic, and simulations, developed using the mechanical theorem prover HOL. Both the predicate-based formulation of temporal logic and the formal theory of simulations have been investigated before in the context of HOL. What is new here is the study of the interaction between the two. In particular, we develop a formal theory of simulations in which certain kinds of temporal properties of the simulating program can be translated into those of the simulated program. Thus, if the simulated program is hard to reason about but the simulating program is easy to reason about, then our theory enables us to perform as much reasoning as possible about the “easy” program and then translate the results back to the “hard” program. The translatable temporal properties include many useful liveness properties.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ching-Tsun Chou, “A Bug in the Distributed Minimum Spanning Tree Algorithm of Gallager, Humblet and Spira”, unpublished note, 1988.Google Scholar
  2. 2.
    Ching-Tsun Chou, “A Sequent Formulation of a Logic of Predicates in HOL”, pp. 71–80 of [3].Google Scholar
  3. 3.
    Luc J.M. Claesen and Michael J.C. Gordon (eds.), Higher Order Logic Theorem Proving and Its Applications, North-Holland, 1993.Google Scholar
  4. 4.
    R.G. Gallager, P.A. Humblet and P.M. Spira, “A Distributed Algorithm for Minimum-Weight Spanning Trees”, in ACM Trans. on Programming Languages and Systems, Vol. 5, No. 1, pp. 66–77, Jan. 1983.Google Scholar
  5. 5.
    Michael J.C. Gordon and Tom F. Melham (eds.), Introduction to HOL: A Theorem-Proving Environment for Higher-Order Logic, Cambridge University Press, 1993.Google Scholar
  6. 6.
    Leslie Lamport, “The Temporal Logic of Actions”, DEC SRC Research Report 79, Dec. 1991.Google Scholar
  7. 7.
    Paul Loewenstein, “A Formal Theory of Simulations between Infinite Automata”, pp. 227–246 of [3].Google Scholar
  8. 8.
    Nancy A. Lynch and Frits W. Vaandrager, “Forward and Backward Simulations, Part I: Untimed Systems”, CWI Report CS-R9313, 1993.Google Scholar
  9. 9.
    J. von Wright, “Mechanising the Temporal Logic of Actions in HOL”, in Proc. of the HOL Tutorial and Workshop, 1991.Google Scholar
  10. 10.
    J. von Wright and T. Långbacka, “Using a Theorem Prover for Reasoning about Concurrent Algorithms”, in Proc. of Workshop on Computer-Aided Verification, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ching-Tsun Chou
    • 1
  1. 1.Computer Science DepartmentUniversity of California at Los AngelesLos AngelesUSA

Personalised recommendations