Abstract
The formalism of Temporal logic is suggested as an appropriate tool for formalizing the semantics of concurrent programs. A simple model of concurrent program is presented in which n processors are executing concurrently n disjoint programs under a shared memory environment. The semantics of such a program specifies the class of state sequences which are admissible as proper execution sequences under the program.
The two main criteria which are required are
a) Each state is obtained from its predecessor in the sequence by exactly one processor performing an atomic instruction in its process.
b) Fair Scheduling: No processor which is infinitely often enabled will be indefinitely delayed.
The basic elements of Temporal Logic are introduced in a particular logic framework DX. The usefulness of Temporal Logic notation in describing properties of concurrent programs is demonstrated. A construction is then given for assigning to a program P a temporal formula W(P) which is true on all proper execution sequences of P. In order to prove that a program P possesses a property R, one has only to prove the implication W(P)⊃R.
An example of such proof is given. It is then demonstrated that specification of the Temporal character of the program's behavior is absolutely essential for the unabiguous undestanding of the meaning of programming constructs.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Brinch Hausen, P.: "A Comparison of Two Synchronizing Concepts", Acta Informatica 1 (1972) 190–199.
Büchi, J.R.: "On a Decision Method in Restricted Second Order Arithmetic", International Congress on Logic Methodology and Philosophy of Science, Stanford, California (1960).
Bull, R.A.: "An Algebraic Study of Diodorean Modal Systems", Journal of Symbolic Logic 30 (1965) 58–64.
Burstall, R.M.: "Formal Description of Program Structure and Semantics of First Order Logic", Machine Intelligence 5(1970) 79–98.
Dummet, M.A. and Lemmon, E.J.: "Modal Logic between S4 and S5" Zeitschrift für Math. Logik ünd Gründ, der Mathematics 5(1959) 250–264.
Francez, N. and Pnueli, A.: "The Analysis of Cyclic Programs", Acta Informatica 9(1978) 133–157.
Gries, D.: "A Proof of Correctness of Reim's Semaphore Implementation of the With-When statement". Technical Report TR 77–314, Cornell University, Ithaca, N.Y. 14853.
Hoare, C.A.R.: "Towards a Theory of Paralle Programming" in Hoare, Perrot (Eds.): Operating Systems Techniques (1972) Academic Press.
Hughes, G.E. and Creswell, M.J.: "An Introduction to Modal Logic", Methuen and Co. London 1972.
Keller, R.M.: Formal Verification of Parallel Programs". CACM 19 (7) 1976.
Krablin, L.: "A Temporal Analysis of Fairness", a forthcoming M.Sc. thesis, University of Pennsylvania.
Kröger, F.: "LAR: A Logic of Algorithmic Reasoning", Acta Informatica 8(1977) 243–266.
Lamport, L.: "Proving the Correctness of Multiprocess Programs", IEEE Transactions on Software Engineering 3(2) 1977, 125–143.
Manna Z: "Properties of Programs and First Order Predicate Calculus", JACM 16 (2) 244–255.
Owicki, S. and Gries, D.: "An Axiomatic Proof Technique for Parallel Programs", Acta Informatica 5, 319–339.
Owicki, S. and Gries, D.: "Verifying Properties of Parallel Programs: An Axiomatic Approach", CACM 19 (5) 1976, 279–284.
Pnueli, A.: "The Temporal Logic of Programs", 19th Annual Symposium on Foundations of Computer Science, Providence R.I. Nov. 1977.
Prior, A.: "Past, Present and Future", Oxford University Press 1967.
Ashcroft, E.A.: "Proving Assertions About Parallel Programs", JCSS 10, 1(1975) 110–135.
Ashcroft, E.A. and Wadge, W.W.: "Intermittent Assertion Proofs in Lucid," IFIP, Toronto 1977.
Kahn, G: "The Semantics of Simple Language for Parallel Proggramming", Proceedings IFIP 14, North Holland.
Harel, D. and Pratt, V.R.: "Nondeterminism in Logics of Programs", Proc. 5th ACM Sumposium on Principles of Programming Languages. Tucson, Ariz. Jan. 1978.
Lamport, L.: "Sometime is sometimes "not never", Technical Report CSL-86, SRI International' Menlo Park, California, Jan. 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pnueli, A. (1979). The temporal semantics of concurrent programs. In: Kahn, G. (eds) Semantics of Concurrent Computation. Lecture Notes in Computer Science, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022460
Download citation
DOI: https://doi.org/10.1007/BFb0022460
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09511-8
Online ISBN: 978-3-540-35163-4
eBook Packages: Springer Book Archive