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In this paper we consider the problem of identifying faulty (crashed) nodes in a wireless sensor network. This problem is of fundamental importance in those applicative scenarios of wireless sensor networks in which battery replacement is feasible. The diagnostic information gathered by operational sensors can be used by an external operator for the sake of network reconfiguration and/or repair; thus extending network lifetime. A fault diagnosis protocol specifically designed for wireless sensor networks is introduced and analyzed. The protocol is proved to be optimal and energy efficient under certain assumptions.