Abstract
Concurrent data structures like stacks, sets or queues need to be highly optimized to provide large degrees of parallelism with reduced contention. Linearizability, a key consistency condition for concurrent objects, sometimes limits the potential for optimization. Hence algorithm designers have started to build concurrent data structures that are not linearizable but only satisfy relaxed consistency requirements.
In this paper, we study quiescent consistency as proposed by Shavit and Herlihy, which is one such relaxed condition. More precisely, we give the first formal definition of quiescent consistency, investigate its relationship with linearizability, and provide a proof technique for it based on (coupled) simulations. We demonstrate our proof technique by verifying quiescent consistency of a (non-linearizable) FIFO queue built using a diffraction tree.
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References
Afek, Y., Korland, G., Natanzon, M., Shavit, N.: Scalable producer-consumer pools based on elimination-diffraction trees. In: D’Ambra, P., Guarracino, M., Talia, D. (eds.) Euro-Par 2010, Part II. LNCS, vol. 6272, pp. 151–162. Springer, Heidelberg (2010)
Afek, Y., Korland, G., Yanovsky, E.: Quasi-linearizability: Relaxed consistency for improved concurrency. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 395–410. Springer, Heidelberg (2010)
Amit, D., Rinetzky, N., Reps, T., Sagiv, M., Yahav, E.: Comparison under abstraction for verifying linearizability. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 477–490. Springer, Heidelberg (2007)
Aspnes, J., Herlihy, M., Shavit, N.: Counting networks. Journal of the ACM 41(5), 1020–1048 (1994)
Colvin, R., Doherty, S., Groves, L.: Verifying concurrent data structures by simulation. ENTCS 137, 93–110 (2005)
de Roever, W., Engelhardt, K.: Data Refinement: Model-Oriented Proof Methods and their Comparison. Cambridge Tracts in Theoretical Computer Science, vol. 47. Cambridge University Press (1998)
Derrick, J., Boiten, E.: Refinement in Z and Object-Z: Foundations and Advanced Applications. Springer (May 2001)
Derrick, J., Boiten, E.A.: Non-atomic refinement in Z. In: Wing, J.M., Woodcock, J., Davies, J. (eds.) FM 1999. LNCS, vol. 1709, pp. 1477–1496. Springer, Heidelberg (1999)
Derrick, J., Schellhorn, G., Wehrheim, H.: Mechanizing a correctness proof for a lock-free concurrent stack. In: Barthe, G., de Boer, F.S. (eds.) FMOODS 2008. LNCS, vol. 5051, pp. 78–95. Springer, Heidelberg (2008)
Derrick, J., Schellhorn, G., Wehrheim, H.: Mechanically verified proof obligations for linearizability. ACM Trans. Program. Lang. Syst. 33(1), 4 (2011)
Derrick, J., Wehrheim, H.: Using coupled simulations in non-atomic refinement. In: Bert, D., Bowen, J.P., King, S., Waldén, M. (eds.) ZB 2003. LNCS, vol. 2651, pp. 127–147. Springer, Heidelberg (2003)
Henzinger, T.A., Kirsch, C.M., Payer, H., Sezgin, A., Sokolova, A.: Quantitative relaxation of concurrent data structures. In: POPL, pp. 317–328. ACM (2013)
Herlihy, M., Shavit, N.: The art of multiprocessor programming. Morgan Kaufmann (2008)
Herlihy, M., Wing, J.M.: Linearizability: A correctness condition for concurrent objects. ACM TOPLAS 12(3), 463–492 (1990)
Lamport, L.: How to make a multiprocessor computer that correctly executes multiprocess programs. IEEE Trans. Computers 28(9), 690–691 (1979)
Reif, W., Schellhorn, G., Stenzel, K., Balser, M.: Structured specifications and interactive proofs with KIV. In: Automated Deduction—A Basis for Applications, Interactive Theorem Proving, vol. II, ch. 1, pp. 13–39. Kluwer (1998)
Schellhorn, G., Wehrheim, H., Derrick, J.: How to prove algorithms linearisable. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 243–259. Springer, Heidelberg (2012)
Shapiro, M., Kemme, B.: Eventual consistency. In: Liu, L., Özsu, M.T. (eds.) Encyclopedia of Database Systems, pp. 1071–1072. Springer US (2009)
Shavit, N.: Data structures in the multicore age. Commun. ACM 54(3), 76–84 (2011)
Tofan, B., Schellhorn, G., Reif, W.: Formal verification of a lock-free stack with hazard pointers. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 239–255. Springer, Heidelberg (2011)
Vafeiadis, V., Herlihy, M., Hoare, T., Shapiro, M.: Proving correctness of highly-concurrent linearisable objects. In: PPoPP 2006, pp. 129–136. ACM (2006)
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Derrick, J., Dongol, B., Schellhorn, G., Tofan, B., Travkin, O., Wehrheim, H. (2014). Quiescent Consistency: Defining and Verifying Relaxed Linearizability. In: Jones, C., Pihlajasaari, P., Sun, J. (eds) FM 2014: Formal Methods. FM 2014. Lecture Notes in Computer Science, vol 8442. Springer, Cham. https://doi.org/10.1007/978-3-319-06410-9_15
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DOI: https://doi.org/10.1007/978-3-319-06410-9_15
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