On Fault Diagnosis of random Free-choice Petri Nets

This paper presents an on-line diagnosis algorithm for Petri nets where a priori probabilistic knowledge about the plant operation is available. We follow the method developed by Benveniste, Fabre, and Haar to assign probabilities to configurations in a net unfolding thus avoiding the need for randomizing all concurrent interleavings of transitions. We consider different settings of the diagnosis problem, including estimating the likelihood that a fault may have happened prior to the most recent observed event, the likelihood that a fault will have happened prior to the next observed event. A novel problem formulation treated in this paper considers deterministic diagnosis of faults that occurred prior to the most recent observed event, and simultaneous calculation of the likelihood that a fault will occur prior to the next observed event

Bayesian network semantics for Petri nets

Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict choices within certain subnets called structural branching cells (s-cells). Bayesian nets (BN) are usually structured as partial orders where nodes define conditional probability distributions. In the paper, we unify the two structures in terms of Symmetric Monoidal Categories (SMC), so that we can apply to PN ordinary analysis techniques developed for BN. Interestingly, it turns out that PN which cannot be SMC-decomposed are exactly s-cells. This result confirms the importance for Petri nets of both SMC and s-cells

Bayesian network semantics for Petri nets

Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict choices within certain subnets called structural branching cells (s-cells). Bayesian nets (BN) are usually structured as partial orders where nodes define conditional probability distributions. In the paper, we unify the two structures in terms of Symmetric Monoidal Categories (SMC), so that we can apply to PN ordinary analysis techniques developed for BN. Interestingly, it turns out that PN which cannot be SMC-decomposed are exactly s-cells. This result confirms the importance for Petri nets of both SMC and s-cells.Fil: Bruni, Roberto. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

Concurrency and Probability: Removing Confusion, Compositionally

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we propose a general solution to this problem based on a recursive, static decomposition of (occurrence) nets in loci of decision, called structural branching cells (s-cells). Each s-cell exposes a set of alternatives, called transactions. Our solution transforms a given Petri net, possibly with confusion, into another net whose transitions are the transactions of the s-cells and whose places are those of the original net, with some auxiliary nodes for bookkeeping. The resulting net is confusion-free by construction, and thus conflicting alternatives can be equipped with probabilistic choices, while nonintersecting alternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped configurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are defined statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency.Fil: Bruni, Roberto Hector. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

Concurrency and Probability: Removing Confusion, Compositionally

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we propose a general solution based on a recursive, static decomposition of (occurrence) nets in loci of decision, called structural branching cells (s-cells). Each s-cell exposes a set of alternatives, called transactions. Our solution transforms a given Petri net into another net whose transitions are the transactions of the s-cells and whose places are those of the original net, with some auxiliary structure for bookkeeping. The resulting net is confusion-free, and thus conflicting alternatives can be equipped with probabilistic choices, while nonintersecting alternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped configurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are defined statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency

Petri nets, probability and event structures

Models of true concurrency have gained a lot of interest over the last decades as models of concurrent or distributed systems which avoid the well-known problem of state space explosion of the interleaving models. In this thesis, we study such models from two perspectives. Firstly, we study the relation between Petri nets and stable event structures. Petri nets can be considered as one of the most general and perhaps wide-spread models of true concurrency. Event structures on the other hand, are simpler models of true concurrency with explicit causality and conflict relations. Stable event structures expand the class of event structures by allowing events to be enabled in more than one way. While the relation between Petri nets and event structures is well understood, the relation between Petri nets and stable event structures has not been studied explicitly. We define a new and more compact unfoldings of safe Petri nets which is directly translatable to stable event structures. In addition, the notion of complete finite prefix is defined for compact unfoldings, making the existing model checking algorithms applicable to them. We present algorithms for constructing the compact unfoldings and their complete finite prefix. Secondly, we study probabilistic models of true concurrency. We extend the definition of probabilistic event structures as defined by Abbes and Benveniste to a newly defined class of stable event structures, namely, jump-free stable event structures arising from Petri nets (characterised and referred to as net-driven). This requires defining the fundamental concept of branching cells in probabilistic event structures, for jump-free net-driven stable event structures, and by proving the existence of an isomorphism among the branching cells of these systems, we show that the latter benefit from the related results of the former models. We then move on to defining a probabilistic logic over probabilistic event structures (PESL). To our best knowledge, this is the first probabilistic logic of true concurrency. We show examples of expressivity achieved by PESL, which in particular include properties related to synchronisation in the system. This is followed by the model checking algorithm for PESL for finite event structures. Finally, we present a logic over stable event structures (SEL) along with an account of its expressivity and its model checking algorithm for finite stable event structures

Probabilistic Cluster Unfoldings

International audienceThis article introduces probabilistic cluster branching processes, a probabilistic unfolding semantics for untimed Petri nets, with no structural or safety assumptions, giving probability measures for concurrent runs. The unfolding is constructed by local choices on each cluster (conflict closed subnet), while the authorization for cluster actions is governed by a stochastic trace, the policy, that authorizes cluster actions. We introduce and characterize stopping times for these models, and prove a strong Markov property. Particularly adaquate probability measures for the choice of step in a cluster, as well as for the policy, are obtained by constructing Markov Fields from suitable marking-dependent Gibbs potentials