On the conceptual foundations of comparative analysis and solution of self-diagnostic problems in multiprocessor systems under different unreliable testing models

We consider self-diagnostics without repair at the system level for multiprocessor (modular) computing systems under multiple permanent faults and with unreliable tests. We distinguish a group of testing models that represent a system with complete but unreliable tests. We formally justify the inclusion relation between models of unreliable tests that lets us unite models into groups with the same diagnostic properties. We prove statements that let us perform comparative analysis of the diagnostic properties for systems that employ different models of unreliable tests. We find the interrelation between the inclusion relation and a known representation of the connection between the syndrome and fault patterns generating it in the form of Boolean functions. We show the efficiency of using Boolean algebra for the comparative analysis of diagnostic properties of systems with different testing models and for the development of local self-diagnostic algorithms.