1. A machine-implementable method for operating a computing system, including plural central electronic complexes processing work units of one or more programs concurrently to control access to data resources shared by at least two central electronic complexes with minimum communication of sharing control parameters, comprising the steps of: maintaining within each complex the interest state of each complex in each of a plurality of resource congruence classes, with a complex having an interest in a congruence class if it has previously granted or waited access to a data resource which is a member of the congruence class; generating within a first complex a first request for access to a resource having a resource key and a resource congruence class; determining the interest state of said first complex and of a second complex in the resource congruence class of the first access request; responsive to the determination that the first complex has an interest and the second complex does not have an interest in the resource congruence class of the first access request, processing the first access request within the first complex; responsive to the second complex having an interest in the resource congruence class of the first access request, communicating the first access request to the second complex for additional processing; responsive to neither complex having an interest in the resource congruence class of the first access request, communicating the new interest state of the first complex in the resource congruence class of the first access request to the second complex, and processing the first access request within the first complex; and the processing of the first access request selectively granting, denying, or waiting access to the resource.