### Backward Reachability Analysis Based on BPNs to Model-Based Diagnosis with Relationships among Symptoms

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#### Abstract

Diagnosing multiple faults that may occur in distributed systems has received a lot of attention over the last decade. In particular, a backward reachability analysis based on Behavioral Petri Net (BPN) models has been proposed to model-based diagnosis of such systems. Nevertheless, it has been defined without tacking into account the concept of precedence relationships that may exist among fault indications or symptoms. The aim of this paper is two fold: first, to extend such analysis to handle precedence orders among symptoms at their signalization time; and second, to deal with the problem of contradictory observations which conduct to an inconsistency in the given problem. The relationships among symptoms are expressed in the net model as transitions among places denoting the corresponding symptoms. For the diagnosis process, they are captured through a novel set of backward firing rules used to construct the corresponding marking graph. In order to treat the inconsistency problems, we propose to restore the required consistency to the given problem. This is accomplished by identifying some symptoms that are known to be absent in the case under examination and when they are supposed present will explain the observed misbehavior. The paper is written in an informal style emphasizing on considerations of practical order than theoretical ones. *Copyright © 2018 Praise Worthy Prize - All rights reserved.*

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