Worst-Case Diagnosis Completeness in Regular Graphs under the PMC Model

  • Authors:
  • Antonio Caruso;Stefano Chessa;Piero Maestrini

  • Affiliations:
  • -;-;-

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 2007

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Abstract

System-level diagnosis aims at the identification of faulty units in a system by the analysis of the system syndrome, that is, the outcomes of a set of interunit tests. For any given syndrome, it is possible to produce a correct (although possibly incomplete) diagnosis of the system if the number of faults is below a syndrome-dependent bound and the degree of diagnosis completeness, that is, the number of correctly diagnosed units, is also dependent on the actual syndrome \sigma. The worst-case diagnosis completeness is a syndrome-independent bound that represents the minimum number of units that the diagnosis algorithm correctly diagnoses for any syndrome. This paper provides a lower bound to the worst-case diagnosis completeness for regular graphs for which vertex-isoperimetric inequalities are known and it shows how this bound can be applied to toroidal grids. These results prove a previous hypothesis about the influence of two topological parameters of the diagnostic graph, that is, the bisection width and the diameter, on the degree of diagnosis completeness.