The Z notation: a reference manual
The Z notation: a reference manual
Linearizability: a correctness condition for concurrent objects
ACM Transactions on Programming Languages and Systems (TOPLAS)
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Practical implementations of non-blocking synchronization primitives
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Nonblocking algorithms and preemption-safe locking on multiprogrammed shared memory multiprocessors
Journal of Parallel and Distributed Computing
Distributed Algorithms
Trace Refinement of Action Systems
CONCUR '94 Proceedings of the Concurrency Theory
Obstruction-Free Synchronization: Double-Ended Queues as an Example
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
A scalable lock-free stack algorithm
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Using elimination to implement scalable and lock-free FIFO queues
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Formal Verification of an Array-Based Nonblocking Queue
ICECCS '05 Proceedings of the 10th IEEE International Conference on Engineering of Complex Computer Systems
Trace-based Derivation of a Lock-Free Queue Algorithm
Electronic Notes in Theoretical Computer Science (ENTCS)
Verifying Michael and Scott's lock-free queue algorithm using trace reduction
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Mechanizing a Correctness Proof for a Lock-Free Concurrent Stack
FMOODS '08 Proceedings of the 10th IFIP WG 6.1 international conference on Formal Methods for Open Object-Based Distributed Systems
Proving linearizability via non-atomic refinement
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
Mechanically verified proof obligations for linearizability
ACM Transactions on Programming Languages and Systems (TOPLAS)
How to prove algorithms linearisable
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
| Hi-index | 0.00 |
We show how a sophisticated, lock-free concurrent stack implementation can be derived from an abstract specification in a series of verifiable steps. The algorithm is a simplified version of one described by Hendler, Shavit and Yerushalmi [Hendler, D., N. Shavit and L. Yerushalmi, A scalable lock-free stack algorithm, in: SPAA 2004: Proceedings of the Sixteenth Annual ACM Symposium on Parallel Algorithms, June 27-30, 2004, Barcelona, Spain, 2004, pp. 206-215], which allows push and pop operations to be paired off and eliminated without affecting the central stack. This reduces contention on the stack compared with other implementations, and allows multiple pairs of push and pop operations to be performed in parallel. Our derivation introduces an abstract model of the elimination process, which allows the basic algorithmic ideas to be separated from implementation details, and provides a basis for explaining and comparing different variants of the algorithm. We show that the elimination stack algorithm is linearisable by showing that any execution of the implementation can be transformed into an equivalent execution of an abstract model of a linearisable stack. At each step in the derivation, this transformation reduces an execution of an entire operation at a time of the model at that level, or two in the case of a successful elimination, rather than translating one atomic action at a time as is done in simulation proofs.