Efficient Execution of Nondeterministic Parallel Programs on Asynchronous Systems

We consider the problem of asynchronous execution of parallel programs. We assume that the original program is designed for a synchronous system, whereas the actual system may be asynchronous. We seek an automatic execution scheme, which allows the asynchronous system to execute the synchronous program. Previous execution schemes provide solutions only for the case where the original program is deterministic. Here, we provide the first solution for the more general case where the original program can be nondeterministic (e.g., randomized). Our scheme is based on a novel agreement protocol for the asynchronous parallel setting. Our protocol allows n asynchronous processors to agree on n word-sized values in O(n log n log log n) total work, assuming an oblivious adversary scheduler. Total work is defined to be the summation of the number of steps performed by all processors (including steps from busy waiting).