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By Jonas Biteus.

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Since agent Rk−1 has already calculated a set of such diagnoses but for agents R1 to Rk−1 , the desired diagnoses can be calculated from the result in Rk−1 and the local diagnoses with cardinality less than or equal L in Rk . Variable l is the number of times that the agent has been called with UpdateAgent(·). The result of the algorithm (variable N) is saved for use by the next agent. If Rk is the last agent and N = ∅ then N is the set of MCMD. E XAMPLE 7: Consider a module where two agents have calculated the PAPER I.

D∈D The set of minimal cardinality diagnoses includes only those diagnoses that include the fewest number of components. When considering repair, it is often natural to start the repair by checking the components included in the diagnoses with the fewest number of components, and then the other diagnoses are checked in increasing number of components. If for example the two diagnoses {A} and {B, C} have been detected. Then, considering only the number of components, component A should first be checked and if this has been found to be normal, the components B and C are checked.

A diagnosis can be seen as special case of a hitting set, which is also denoted vertex cover. D EFINITION 3 (Hitting set): Let F be a set of sets. The set S ⊆ hitting set for the set F if F∈F F is a S∩F=∅ for all F ∈ F. Similar to diagnoses and conflicts, a hitting set S for the set F is a minimal hitting set if there is no proper subset S ′ ⊂ S where S ′ is a hitting set for the set F. From the definitions can be seen that the diagnoses are the hitting sets for the set of conflicts, compare with Theorem 1.

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