Advertisement

Exact and Efficient Verification of Parameterized Cache Coherence Protocols

  • E. Allen Emerson
  • Vineet Kahlon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2860)

Abstract

We propose new, tractably (in some cases provably) efficient algorithmic methods for exact (sound and complete) parameterized reasoning about cache coherence protocols. For reasoning about general snoopy cache protocols, we introduce the guarded broadcast protocols model and show how an abstract history graph construction can be used to reason about safety properties for this framework. Although the worst case size of the abstract history graph can be exponential in the size of the transition diagram of the given protocol, the actual size is small for standard cache protocols as is evidenced by our experimental results. The framework can handle all 8 of the cache protocols in [19] as well as their split-transaction versions. We next identify a framework called initialized broadcast protocols suitable for reasoning about invalidation-based snoopy cache protocols and show how to reduce reasoning about such systems with an arbitrary number of caches to a system with at most 7 caches. This yields a provably polynomial time algorithm for the parameterized verification of invalidation based snoopy protocols. Our results apply to both safety and liveness properties. Finally, we present a methodology for reducing parameterized reasoning about directory based protocols to snoopy protocols, thus leveraging techniques developed for verifying snoopy protocols to directory based ones, which are typically are much harder to reason about. We demonstrate by reducing reasoning about a directory based protocol suggested by German [17] to the ESI snoopy protocol, a modification of the MSI snoopy protocol.

Keywords

Model Check Safety Property Computation Path Memory Block Liveness Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abdulla, P., Cerans, K., Jonsson, B., Tsay, Y.K.: General Decidability Theorems for Infinite State Systems. In: LICS (1996)Google Scholar
  2. 2.
    Abdulla, P., Boujjani, A., Jonsson, B., Nilsson, M.: Handling global conditions in parameterized systems verification. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 134–145. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Abdulla, P., Jonsson, B.: On the existence of network invariants for verifying parameterized systems. In: Olderog, E.-R., Steffen, B. (eds.) Correct System Design. LNCS, vol. 1710, pp. 180–197. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  4. 4.
    Baukus, K., Lakhnech, Y., Stahl, K.: Parameterized Verification of a Cache Coherence Protocols: Safety and Liveness. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 317–330. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Browne, M.C., Clarke, E.M., Grumberg, O.: Reasoning about Networks with Many Identical Finite State Processes. Information and Control 81(1), 13–31 (1989)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Clarke, E.M., Grumberg, O., Hirashi, H., Jha, S., Long, D.E., McMillan, K.L., Ness, L.A.: Verification of the Futurebus+cache coherence protocol. In: Proc. 11th Int. Symp. on Computer Hardware Description Languages and their Applications (1993)Google Scholar
  7. 7.
    Culler, D.E., Singh, J.P.: Parallel Computer Architecture:A Hardware/Software Approach. Morgan Kaufmann Publishers, San Francisco (1998)Google Scholar
  8. 8.
    Delzanno, G.: Automatic Verification of Parameterized Cache Coherence Protocols. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 51–68. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Emerson, E.A., Kahlon, V.: Reducing Model Checking of the Many to the Few. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Emerson, E.A., Kahlon, V.: Model Checking Large-Scale and Parameterized Resource Allocation Systems. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, p. 251. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Emerson, E.A., Kahlon, V.: Rapid Parameterized Model Checking of Snoopy Cache Protocols. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 144–159. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Emerson, E.A., Kahlon, V.: Model Checking Guarded Protocols. In: LICS 2003 (2003)Google Scholar
  13. 13.
    Emerson, E.A., Namjoshi, K.S.: Reasoning about Rings. In: POPL, pp. 85–94 (1995)Google Scholar
  14. 14.
    Emerson, E.A., Namjoshi, K.S.: On Model Checking for Non-Deterministic Infinite-State Systems. In: LICS 1998 (1998)Google Scholar
  15. 15.
    Emerson, E.A., Namjoshi, K.S.: Automatic Verification of Parameterized Synchronous Systems. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, Springer, Heidelberg (1996)Google Scholar
  16. 16.
    Esparza, J., Finkel, A., Mayr, R.: On the Verification of Broadcast Protocols. In: LICS 1999 (1999)Google Scholar
  17. 17.
    German, S.M.: Private communicationGoogle Scholar
  18. 18.
    German, S.M., Sistla, A.P.: Reasoning about Systems with Many Processes. J. ACM 39(3) (July 1992)Google Scholar
  19. 19.
    Handy, J.: The Cache Memory Book. Academic Press, London (1993)zbMATHGoogle Scholar
  20. 20.
    Kurshan, R.P., McMillan, K.L.: A Structural Induction Theorem for Processes. In: PODC, pp. 239–247 (1989)Google Scholar
  21. 21.
    Maidl, M.: A Unifying Model Checking Approach for Safety Properties of Parameterized Systems. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 311. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    McMillan, K., Schwalbe, J.: Formal Verification of the Gigamax Cache Consistency Protocol. In: Proc. Int. Symp. on Shared Memory Multiprocessors, pp. 242–251 (1991)Google Scholar
  23. 23.
    Pnueli, A., Ruah, S., Zuck, L.: Automatic Deductive Verification with Invisible Invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, p. 82. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  24. 24.
    Pong, F., Dubois, M.: A New Approach for the Verification of Cache Coherence Protocols. IEEE Transactions on Parallel and Distributed Systems 6(8) (August 1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • E. Allen Emerson
    • 1
  • Vineet Kahlon
    • 1
  1. 1.Department of Computer Sciences and Computer Engineering Research CenterThe University of TexasAustinUSA

Personalised recommendations