Correctness and concurrent complexity of the Black-White Bakery Algorithm

Lamport’s Bakery Algorithm (Commun ACM 17:453–455, 1974) implements mutual exclusion for a fixed number of threads with the first-come first-served property. It has the disadvantage, however, that it uses integer communication variables that can become arbitrarily large. Taubenfeld’s Black-White Bakery Algorithm (Proceedings of the DISC. LNCS, vol 3274, pp 56–70, 2004) keeps the integers bounded, and is adaptive in the sense that the time complexity only depends on the number of competing threads, say N. The present paper offers an assertional proof of correctness and shows that the concurrent complexity for throughput is linear in N, and for individual progress is quadratic in N. This is proved with a bounded version of UNITY, i.e., by assertional means

Verifying a simplification of mutual exclusion by Lycklama-Hadzilacos

<p>A simplification of the mutual exclusion algorithm of Lycklama and Hadzilacos (ACM Trans Program Lang Syst 13:558-576, 1991) is presented. It uses only four nonatomic shared bits per thread to guarantee mutual exclusion with the first-come-first-served property. The algorithm is verified by assertional methods, aided by the proof assistant PVS. A variation with five bits per thread is also given. This variation may give better performance when the number of threads is large. The use of the proof assistant made it easy to transfer the proof of the main algorithm to the variation.</p>