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This paper is concerned with the diagnosability property of partially observed Discrete Event Systems (DES) modeled by live and safe Interpreted Petri Nets (IPN). The IPN are used to model the normal behavior and permanent behavior. Based on the model with the normal and faulty behavior, the notion of input-output diagnosability is introduced and a polynomial algorithm to characterize diagnosable IPN is proposed. The novel features of the approach herein presented are: a) the notion of maximum relative distance between any pair of transitions; b) the use of the net siphons and T-semiflows to determine the relative distance between any pair of transitions; c) a characterization of diagnosable IPN based on the relative distance concept, it characterizes a broader class of IPN exhibiting the diagnosability property and presents a better deepening of the structures needed to characterize diagnosable IPN; d) an efficient method for obtaining a reduced diagnoser IPN model is proposed.