Skip to main content
SpringerLink
Log in

An approach to automating the verification of compact parallel coordination programs. I

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

A class of parallel coordination programs for a shared memory asynchronous parallel processor is considered. These programs use the operation Fetch & Add which is the basic primitive for the NYU-Ultracomputer. A correctness proof for the considered programs must be done for arbitrary number N of processing elements since the Ultracomputer design includes thousands of PEs.

A reachability set description (RSD) is introduced, in which all reachable states of a program (exponential function of N) are collapsed into a fixed number of metastates. The transitions between these metastates are then specified. By using such notation, it becomes feasible to prove various temporal properties of a parallel program, in particular, the absence of livelock. The concept of a compact parallel program is introduced. Roughly speaking a parallel program executed by N PEs is compact if there exists a boundary T independent of N such that any state of this program is reachable within time T. Compactness may also be understood as the finiteness of the expansion for the strongest invariant in the least fixpoint theory, where such finiteness is uniform over N. A program that builds RSDs for compact parallel programs and examples of proofs generated by this program are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ashcroft, E.A.: Proving assertions about parallel programs. Journ. Comput. System Sci. 10, 110–135 (1975)

    Google Scholar 

  2. Ben-Ari, M.: Temporal logic proofs of concurrent programs. Dept. Appl. Math., Weizmann Institute of Science, Report CS82-12, 1982

  3. Clarke, E.M.: Synthesis of resource invariants for concurrent programs. ACM Trans. on Programming Languages and Systems. 2 (3), 338–358 (1980)

    Google Scholar 

  4. Courtois, P.J., Heymans, F., Parnas, D.L.: Concurrent control with ‘readers’ and ‘writers’. Comm. ACM 14, 667–668 (1971)

    Google Scholar 

  5. Dijkstra, E.M.: Hierarchical orderings of sequential processes. Acta Informat. 1, 115–138 (1971)

    Google Scholar 

  6. Genrich, H.J., Lautenbach, K.: System modeling with high-level Petri Nets. Theor. Comput. Sci. 13, 109–136 (1981)

    Google Scholar 

  7. Gottlieb, A., Grishman, R., Kruskal, C.P., McAuliffe, K.P., Rudolph, L., Snir, M.: The NYU Ultracomputer-designing an MIMD shared memory parallel computer. IEEE Trans. Computers, Vol. C-32, No. 2, February 1983

  8. Gottlieb, A., Lubachevsky, B.D., Rudolph, L.: Basic techniques for the efficient coordination of very large numbers of cooperating sequential processors. ACM Trans, on Comput. Lang. Sys. 5 (2), 164–189 (1983)

    Google Scholar 

  9. Habermann, A.N.: Synchronization of communicating processes. Comm. ACM. 15 (3), 171–176 (1972)

    Google Scholar 

  10. Hopcroft, J., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Comput. Sci. 8, 135–159 (1979)

    Google Scholar 

  11. Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. System. Sci. 3, 147–195 (1969)

    Google Scholar 

  12. Kwong, Y.S.: On the absence of livelocks in parallel programs. In: Semantics of Concurrent Computation. (G. Goos, J. Hartmanis, eds.) Proc. of the Int. Symp., Lecture Notes in Computer Science 70, pp. 172–190. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  13. Lamport, L.: Proving the correctness of multiprocess programs. IEEE Trans. Softw. Eng. 3, 125–143 (1977)

    Google Scholar 

  14. Lubachevsky, B.D.: Verification of several parallel coordination programs based on descriptions of their reachability sets. Ultracomputer Note # 33, Courant Institute, New York University, July, 1981

  15. Morris, J.M.: A starvation-free solution to the mutual exclusion problem. Information Processing Lett. 8, 76–80 (1979)

    Google Scholar 

  16. Owicki, S., Gries, D.: Verifying properties of parallel programs: an axiomatic approach. Comm. ACM 19, No. 5, p. 279–285 (May 1976)

    Google Scholar 

  17. Owicki, S., Gries, D.: An axiomatic proof technique for parallel programs. I. Acta Informat. 6, 319–340 (1976)

    Google Scholar 

  18. Owicki, S., Lamport, L.: Proving liveness properties of concurrent programs. ACM Trans. Prog. Lang, and Syst. 3, vol. 4 (July 1982)

  19. Park, D.: Fixpoint induction and proofs of program properties. In: Machine Intelligence (B. Meltzer and D. Michie, eds.) 5, 59–78. Edinburgh: University Press 1969

    Google Scholar 

  20. Pnueli, A.: The temporal semantics of concurrent programs. Theor. Comput Sci. 13, 45–60 (1981)

    Google Scholar 

  21. Rudolph, L.: Software structures for ultraparallel computings. Ph.D. Thesis, Courant Inst., NYU, 1982

  22. Schwartz, J.T.: Ultracomputers. ACM Trans, on Prog. Lang. Sys. pp. 484–521 (1980)

  23. Schwartz, R.L., and Melliar-Smith, P.M.: Temporal logic specification of distributed systems. Proc. 2-nd Int. Conf. on Distributed Computing Systems, pp. 446–454. Paris, April 1981

  24. Shaw, A.C.: The logical design of operating systems Englwood Cliffs: Prentice-Hall, 1974

    Google Scholar 

  25. Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5, 285–309

  26. Thau, R.: Private communication.

  27. van Lamsweerde, A., Sintzoff, M.: Formal derivation of strongly correct concurrent programs. Acta Informat. 12, 1–31 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, New York University, 251 Mercer St., 10012, New York, NY, USA

    Boris D. Lubachevsky

Authors
  1. Boris D. Lubachevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract No. DE-AC02-76ER03077, and in part by the National Science Foundation under Grant No. NSF-MCS79-21258

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lubachevsky, B.D. An approach to automating the verification of compact parallel coordination programs. I. Acta Informatica 21, 125–169 (1984). https://doi.org/10.1007/BF00289237

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289237

Keywords

Search

Navigation