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Randomized mutual exclusion algorithms revisited

In [4] a randomized algorithm for mutual exclusion with bounded waiting, employing a logarithmic sized shared variable, was given. Saias and Lynch [5] pointed out that the adversary scheduler postulated in the above paper can observe the behavior of processes in the interval between an opening of the critical section and the next closing of the critical section. it can then draw conclusions about values of their local variables as well as the value of the randomized round number component of the shared variable, and arrange the schedule so as to discriminate against a chosen process. This invalidates the claimed properties of the algorithm.
In the present paper the algorithm in [4] is modified, using the ideas of [4], so as to overcome this difficulty, obtaining essentially the same results. Thus, as in [4], randomization yields simple algorithms for mutual-exclusion with bounded waiting, employing a shared variable of considerably smaller size than the lower-bound established in [1] for deterministic algorithms.