Ideal arbiters: Analysis and design

An ideal arbiter for concurrent processes that share a resource ensures the mutual exclusion of the users, is fair, and grants requests in the order that they were made. Non-ideal arbitration schemes, both of algorithmic and circuit form, with the first two properties are well-known. Here we study ideal arbiters in a top-down manner, at three levels of abstraction: behavioral properties expressed in temporal logic, discrete-time automata, and Boolean circuits and functions. We show that an n-process arbiter can be realized with complexity O(n
²
log n) and delay O(log n). The goodness of these results is examined from a viewpoint of Boolean complexity theory. We also study a two-level modular realization of the arbiter, equivalent to the above monolithic one. If the equivalence is not required to hold under worst-case user behavior, the modular arbiter can be implemented with much smaller complexity than the monolithic one and with comparable delay.