Diagnosis of Symmetric Graphs Under the BGM Model

This paper addresses the problem of the identification of faulty units in symmetric systems under the diagnostic model proposed by Barsi, Grandoni and Maestrini (hence called the BGM model). The paper introduces and evaluates an algorithm named Diagnosis Algorithm for Symmetric Systems under the BGM model (DABS). It is shown that DABS provides a diagnosis unconditionally correct although possibly incomplete. A measure of diagnosis incompleteness IDeg(t) has been defined as the quotient between the number of suspect units (i.e. the units that DABS is unable to identify as either good or faulty) and the number of system units. IDeg(t) is evaluated over the set of syndromes deriving from at most t faults under the BGM model. A general approach to the evaluation of IDeg(t) in symmetric systems is introduced, and tight bounds to IDeg(t) are derived for square toroidal grids and hypercubes. This bound is O(t/n) in the case of square toroidal grids of n units.