Linear recognition problems with exclusion

We consider linear recognition problems with exclusion (LRP with exclusion) that are test models of some classes of problems of discrete optimization and parametric linear programming. The test approach to the solution of LRP with exclusion is based on the concept of a partitioning set (PS) of the problem. The description of the set of all PS of LRP with exclusion is considerably simplified if it is known that it has exactly one deadlock PS. We show that for any LRP with exclusion either there exists a single deadlock PS or the set of deadlock PS has the power of a continuum. We find conditions for uniqueness.