72 Int. J. Computational Science and Engineering, Vol. 18, No. 1, 2019 Copyright © 2019 Inderscience Enterprises Ltd. Distributed diagnosis based on distributed probability propagation nets Yasser Moussa Berghout* and Hammadi Bennoui LINFI Lab. and Department of Computer Science, University of Biskra, 07000, Biskra, Algeria Email: ber.yasser@gmail.com Email: bennoui@gmail.com *Corresponding author Abstract: This paper addresses the problem of modelling uncertainty in the distributed context. It is situated in the field of diagnosis; more precisely, model-based diagnosis of distributed systems. A special focus is given to modelling uncertainty and probabilistic reasoning. Thus, this work is based on a probabilistic modelling formalism called: ‘probability propagation nets’ (PPNs), which are designed for centralised systems. Hence, an extension of this model is proposed to suit the distributed context. Distributed probability propagation nets (DPPNs), the proposed extension, were conceived to consider the distributed systems’ particularities. So, the set we consider is a set of interacting subsystems, each of which is modelled by a DPPN. The interaction among the subsystems is modelled through the firing of common transitions belonging to more than one subsystem. All of that is logically supported by means of probabilistic Horn abductions (PHAs). Furthermore, the diagnostic process is done by exploiting transition-invariants, a diagnostic technique developed for Petri nets. The proposed extension is illustrated through a real life example. Keywords: model-based diagnosis; distributed systems; probabilistic reasoning; probability propagation nets; PPNs; probabilistic Horn abduction; PHA; Petri nets; transition invariants; causal models. Reference to this paper should be made as follows: Berghout, Y.M. and Bennoui, H. (2019) ‘Distributed diagnosis based on distributed probability propagation nets’, Int. J. Computational Science and Engineering, Vol. 18, No. 1, pp.72–79. Biographical notes: Yasser Moussa Berghout is currently a PhD student in Artificial Intelligence at the University of Biskra. He received his Master’s in Mobile Intelligent Systems from the University of Batna. His research interests include uncertainty modelling, distributed systems, diagnosis and artificial intelligence in general. Hammadi Bennoui is with the Department of Computer Science, Faculty of Exact, Natural and Life Sciences, University of Biskra, in Algeria. He received his Engineer degree in Computer Science in 1994 and Magister degree in 2000 from the University of Constantine. From 2000, he is a Lecturer at the University of Biskra. He served as the Department Head of the Computer Science Department during the years 2006 and 2007. He obtained his PhD degree in 2012 and HDR in 2013 from the same university. Since then, he is an Associate Professor in Computer Science Department at the Biskra University. His field of research includes model-based diagnosis of distributed systems, Petri nets analysis, specification and verification of distributed systems. This paper is a revised and expanded version of a paper entitled ‘Introduction to distributed probability propagation nets’ presented at International conference on Intelligent Information Processing, Security and Advanced Communication, Batna, Algeria, 23–25 November 2015. 1 Introduction Real life systems such as: the internet, industrial manufacturers and telecommunication networks, tend to be more and more distributed. They are headed towards ubiquity and omnipresence, in the pursuit of Weiser’s (1991) vision: “The most profound technologies are those that disappear. They weave themselves into the fabric of everyday life until they are indistinguishable from it”. This trend comes with a lot of challenges such as: management, security and reliability of complex systems. The importance of the diagnosis of distributed systems arises from the fact that these systems are not perfect, they are expected to fall down at some point. Thus, locating the sources of malfunctions could be critical to the reliability and omnipresence of a system. It is the first step to deal with a