Abstract
Transactional memory (TM) is a mechanism that manages thread synchronisation on behalf of a programmer so that blocks of code execute with the illusion of atomicity. The main safety criterion for transactional memory is opacity, which defines conditions for serialising concurrent transactions.
Verifying opacity is complex because one must not only consider the orderings between fine-grained (and hence concurrent) transactional operations, but also between the transactions themselves. This paper presents a sound and complete method for proving opacity by decomposing the proof into two parts, so that each form of concurrency can be dealt with separately. Thus, in our method, verification involves a simple proof of opacity of a coarse-grained abstraction, and a proof of linearizability, a better-understood correctness condition. The most difficult part of these verifications is dealing with the fine-grained synchronization mechanisms of a given implementation; in our method these aspects are isolated to the linearizability proof. Our result makes it possible to leverage the many sophisticated techniques for proving linearizability that have been developed in recent years. We use our method to prove opacity of two algorithms from the literature. Furthermore, we show that our method extends naturally to weak memory models by showing that both these algorithms are opaque under the TSO memory model, which is the memory model of the (widely deployed) x86 family of processors. All our proofs have been mechanised, either in the Isabelle theorem prover or the PAT model checker.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In this paper, we use the word ‘operation’ in two senses. Here, we mean ‘operation’ as a component of the TM interface. Later, we use ‘operation’ to mean the instance of an operation within an execution. Both senses are standard, and any ambiguity is resolved by the context.
- 2.
Note: this differs from the real-time order on transactions defined in Sect. 2.
References
Adve, S.V., Aggarwal, J.K.: A unified formalization of four shared-memory models. IEEE Trans. Parallel Distrib. Syst. 4(6), 613–624 (1993)
Armstrong, A., Dongol, B., Doherty, S.: Reducing opacity to linearizability: a sound and complete method. arXiv e-prints (October 2016). https://arxiv.org/abs/1610.01004
Attiya, H., Gotsman, A., Hans, S., Rinetzky, N.: A programming language perspective on transactional memory consistency. In: Fatourou, P., Taubenfeld, G. (eds.) PODC 2013, pp. 309–318. ACM (2013)
Bouajjani, A., Emmi, M., Enea, C., Hamza, J.: On reducing linearizability to state reachability. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 95–107. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47666-6_8
Černý, P., Radhakrishna, A., Zufferey, D., Chaudhuri, S., Alur, R.: Model Checking of linearizability of concurrent list implementations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 465–479. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14295-6_41
Chakraborty, S., Henzinger, T.A., Sezgin, A., Vafeiadis, V.: Aspect-oriented linearizability proofs. Logical Methods Comput. Sci. 11(1) (2015)
Dalessandro, L., Dice, D., Scott, M., Shavit, N., Spear, M.: Transactional mutex locks. In: D’Ambra, P., Guarracino, M., Talia, D. (eds.) Euro-Par 2010. LNCS, vol. 6272, pp. 2–13. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15291-7_2
Dalessandro, L., Spear, M.F., Scott, M.L.: NORec: streamlining STM by abolishing ownership records. In: Govindarajan, R., Padua, D.A., Hall, M.W. (eds.) PPoPP, pp. 67–78. ACM (2010)
Derrick, J., Dongol, B., Schellhorn, G., Travkin, O., Wehrheim, H.: Verifying opacity of a transactional mutex lock. In: Bjørner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 161–177. Springer, Cham (2015). doi:10.1007/978-3-319-19249-9_11
Doherty, S., Groves, L., Luchangco, V., Moir, M.: Formal verification of a practical lock-free queue algorithm. In: Frutos-Escrig, D., Núñez, M. (eds.) FORTE 2004. LNCS, vol. 3235, pp. 97–114. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30232-2_7
Doherty, S., Groves, L., Luchangco, V., Moir, M.: Towards formally specifying and verifying transactional memory. Formal Asp. Comput. 25(5), 769–799 (2013)
Dongol, B., Derrick, J.: Verifying linearisability: a comparative survey. ACM Comput. Surv. 48(2), 19 (2015)
Guerraoui, R., Henzinger, T.A., Singh, V.: Model checking transactional memories. Distrib. Comput. 22(3), 129–145 (2010)
Guerraoui, R., Kapalka, M.: On the correctness of transactional memory. In: Chatterjee, S., Scott, M.L. (eds.) PPoPP, pp. 175–184. ACM (2008)
Guerraoui, R., Kapalka, M.: Principles of Transactional Memory. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, San Rafael (2010)
Harris, T., Larus, J.R., Rajwar, R.: Transactional Memory. Synthesis Lectures on Computer Architecture, 2nd edn. Morgan & Claypool Publishers, San Rafael (2010)
Herlihy, M., Wing, J.M.: Linearizability: a correctness condition for concurrent objects. ACM TOPLAS 12(3), 463–492 (1990)
Hoare, C.A.R.: Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)
Koskinen, E., Parkinson, M.: The push/pull model of transactions. In: PLDI. PLDI 2015, vol. 50, pp. 186–195. ACM, New York, NY, USA, June 2015
Lesani, M., Luchangco, V., Moir, M.: A framework for formally verifying software transactional memory algorithms. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 516–530. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32940-1_36
Lesani, M., Luchangco, V., Moir, M.: Putting opacity in its place. In: Workshop on the Theory of Transactional Memory (2012)
Lesani, M., Palsberg, J.: Decomposing opacity. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 391–405. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45174-8_27
Liu, Y., Chen, W., Liu, Y.A., Sun, J., Zhang, S.J., Dong, J.S.: Verifying linearizability via optimized refinement checking. IEEE Trans. Softw. Eng. 39(7), 1018–1039 (2013)
Owens, S.: Reasoning about the implementation of concurrency abstractions on x86-TSO. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 478–503. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14107-2_23
Schellhorn, G., Derrick, J., Wehrheim, H.: A sound and complete proof technique for linearizability of concurrent data structures. ACM TOCL 15(4), 31:1–31:37 (2014)
Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: towards flexible verification under fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709–714. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02658-4_59
Vafeiadis, V.: Modular fine-grained concurrency verification. Ph.D. thesis. University of Cambridge (2007)
Acknowledgements
We thank John Derrick for helpful discussions and funding from EPSRC grant EP/N016661/1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 IFIP International Federation for Information Processing
About this paper
Cite this paper
Armstrong, A., Dongol, B., Doherty, S. (2017). Proving Opacity via Linearizability: A Sound and Complete Method. In: Bouajjani, A., Silva, A. (eds) Formal Techniques for Distributed Objects, Components, and Systems. FORTE 2017. Lecture Notes in Computer Science(), vol 10321. Springer, Cham. https://doi.org/10.1007/978-3-319-60225-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-60225-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60224-0
Online ISBN: 978-3-319-60225-7
eBook Packages: Computer ScienceComputer Science (R0)
