Abstract
We have shown that correctness properties of parallel programs can be described using computation trees and that from these descriptions fixpoint characterizations can be generated. We have also given conditions on the form of computation tree descriptions to ensure that a correctness property can be characterized using continuous fixpoints. A consequence is that a correctness property such as inevitability under fair scheduling can be characterized as the least fixpoint of a monotonic, noncontinuous transformer, but cannot be characterized using fixpoints of continuous transformers (nor as the greatest fixpoint of a monotonic transformer of any degree of complexity lower than fair inevitability itself). Hence, currently known proof rules are not applicable (see however [FS80]). We are now investigating whether useful proof rules can exist for correctness properties having only a monotonic, noncontinuous least fixpoint characterization. In addition, we are examining alternate notions of fairness which do have continuous fixpoint characterizations.
This work was partially supported by NSF Grant MCS-7908365
This is a preview of subscription content, access via your institution.
Preview
Unable to display preview. Download preview PDF.
8. References
Basu, S.K. and Yeh, R.T., Strong Verification of Programs. IEEE Trans. on Software Engineering, v. SE-1. no. 1, pp.339–354, September 1975.
Chandra, A. K., Computable Nondeterministic Functions. 19th Annual Symp. on Foundations of Computer Science, 1978.
Clarke, E. M., Program Invariants as Fixpoints. 18th Annual Symp. on Foundations of Computer Science, 1977.
Clarke, E. M., Synthesis of Resource Invariants for Concurrent Programs, 6th POPL Conference, January, 1979.
Cousot, P. and Cousot R., Static Determination of Dynamic Properties of Programs. Proc. 2nd Int. Symp. on Programming, (B. Robinet, ed.), Dunod, Paris, April 1976.
de Bakker, J. W., Recursive Programs as Predicate Transformers. Mathematical Centre, Amsterdam, 1977.
de Bakker. J. W., Semantics of Infinite Processes Using Generalized Trees. Mathematical Centre, Amsterdam, 1977.
Dijkstra, E. W., A Discipline of Programming, Prentice-Hall, 1976.
Flon, L. and Suzuki, N., Consistent and Complete Proof Rules for the Total Correctness of Parallel Programs. 19th Annual Symp. on Foundations of Computer Science, 1978.
Flon, L. and Suzuki, N., The Total Correctness of Parallel Programs. SIAM J. Comp., to appear
Hinman, P. G., Recursion-Theoretic Hierarchies, Springer-Verlag, Berlin, 1978.
Hoare, C. A. R., An Axiomatic Approach to Computer Programming CACM, v.10. no 12., pp.322–329, October 1969.
Meyer, A. R. and Winklmann, K., On the Expressive Power of Dynamic Logic. Proceedings of the 11th Annual ACM Symp. on Theory of Computing, 1979.
Park, D., Fixpoint Induction and Proofs of Program Properties, in Machine Intelligence 5, (D. Mitchie, ed.) Edinburgh University Press, 1970.
Reif, J. H., Data Flow Analysis of Communicating Processes. 6th POPL Conference, January 1979.
Rogers, H. R., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967.
Sintzoff, M. and Van Lamsweerde, A., Formal Derivation of Strongly Correct Parallel Programs, M. B. L. E. Research Lab., Brussels, Report R338, October 1976.
Tarski, A., A Lattice-Theoretical Fixpoint Theorem and Its Applications. Pacific J. Math., 5, pp.285–309 (1955).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emerson, E.A., Clarke, E.M. (1980). Characterizing correctness properties of parallel programs using fixpoints. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_69
Download citation
DOI: https://doi.org/10.1007/3-540-10003-2_69
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10003-4
Online ISBN: 978-3-540-39346-7
eBook Packages: Springer Book Archive