Read-Write Reductions

The discovery, more than a decade ago, of the relation between DistributedComputing (DC) and Algebraic-Topology (AT) raised the specter of requiring checking task solvability to be intimately connected to expertise in AT. Yet, in the area of Centralized Algorithms proving a problem to be NP or PSPACE complete requires more algorithmic expertise than complexity one. In analogy, we show that in DC the equivalent of polynomial-time reductions, is read-write reductions. We define the notion of read-write reduction between distributed tasks, and show that all interesting known read-write impossible tasks can be proven impossible via read-write reduction to a task called Symmetry-Breaking (SB). Discovering a read-write reduction requires solely algorithmic expertise.