Ambiguity of choosing

Abstract

We consider a model in which communication is by means of asynchronous, atomic reads and writes of shared memory. One of our main results is a lemma showing that a single fail-stop failure can lead to ambiguity whenever a choice must be made. This lemma can be used to prove a variety of impossibility results and lower bounds. We use the lemma to give a simple proof of the optimality of our solution to the l-assignment problem. The l-assignment problem requires that a group of processors compete for a pool of distinct resources with the restriction that a limited number of processors can halt unexpectedly. (The problem differs from the normal l-exclusion problem in that an explicit assignment of resources must be made.) Use of the lemma is also demonstrated by giving a simple proof for the lower bound of the pure buffers version of the concurrent reading while writing problem.