Reduction methods developed by Lipton, Lamport, Cohen, and others, allow one to reason about concurrent programs at various levels of atomicity. An action which is considered to be atomic at one level may be implemented by more complex code at the next level. We can show that certain properties of the program are preserved by first showing that the property holds when the expanded code is executed sequentially, and then showing that any execution in which this code is executed concurrently with other processes is equivalent to an execution in which the expanded code is executed without interruption.

Existing reduction methods are aimed at traditional approaches to concurrency which prevent interference between concurrent processes using mechanisms such as locks or semaphores. In this paper, we show that these reduction methods can be adapted to reason about nonblocking algorithms, which are designed to operate correctly in the presence of interference, rather than to avoid interference. These algorithms typically use strong synchronisation primitives, such as Load Linked/Store Conditional or Compare and Swap, to detect that interference has occurred and in that case retry their operations. We show that reduction can be used with such algorithms, and illustrate this approach with examples based on shared counters and stacks.