Wait - free Test - and - Set ( Extended

This paper presents an economical, randomized, wait-free construction of an n-process test-and-set bit from read write registers. The test-and-set shared object has two atomic operations, test&set, which atomically reads the bit and sets its value to 1, and the reset operation that resets the bit to 0. We identify two new complexity measures by which to evaluate wait-free algorithms: (a) The amount of randomness used, and (b) `Parallel-Time'|the maximum sequential depth of an execution (i.e. longest chain of operations that must precede each other). The previously best known algorithm for n-process test-and-set Her91] takes an expected (n 2) parallel time, and (n 4) sequential time per operation, and (n 2 log n) space per processor. In contrast, our direct implementation improves this on all counts by using O(log n) coin ips, O(log n) parallel time, O(n) sequential time, per operation, and O(n) space per processor. Thus the question on the diierence in the expected complexity of randomized constructions of concurrent objects from read/write registers is raised.