Solvability Characterization for General Three-Process Tasks

A key result of distributed computing in asynchronous systems is a characterization for the wait-free solvability of colorless tasks by the existence of a continuous map from the task's input complex (representing the valid input configurations) to its output complex (representing the valid output configurations) which respects that task's specification. This natural characterization led to many proofs, mainly of impossibility: showing that a colorless task is not wait-free solvable, can be done by proving that there is no continuous map (respecting the task's specification) between two simplicial complexes, which can be done using classical topological machinery.