The computational structure of progress conditions and shared objects

We study the effect of different progress conditions on the computability of distributed systems. For a system with n processes, we define exponentially many new progress conditions and explore their properties and relative strength. We cover many known and new interesting conditions and propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. Comparing our classification with the traditional one, which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Together with our technical results, the new definitions provide a deeper understanding of synchronization and concurrency.