Affine Tasks for k-Test-and-Set

The paper proposes a surprisingly simple characterization of a classical class of models of distributed computing, captured by an affine task : A subcomplex of the second iteration of the standard chromatic subdivision. We show that the class of affine task we propose has an element equivalent, regarding task solvability, to any wait-free shared-memory model in which processes have additionally access to k-test-and-set objects. Our results thus extend existing affine characterization beyond fair models