Basis marking representation of Petri net reachability spaces and its application to the reachability problem

In this paper a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions, in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings. We show that to determine a max-cardinality-T_I basis partition is an NPhard problem, but a max-set-T_I basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally this approach is further extended to unbounded nets

Diagnosis on a sliding window for partially observable Petri nets

summary:In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length $h$. Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. The proposed approach consists in exploiting a subset of $h$ observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a "forgetfulness" of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As the analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these irrelevant basis markings based on linear programming is proposed

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

On the Equivalence of Observation Structures for Petri Net Generators

Observation structures considered for Petri net generators usually assume that the firing of transitions may be observed through a static mask and that the marking of some places may be measurable. These observation structures, however, are rather limited, namely they do not cover all cases of practical interest where complex observations are possible. We consider in this paper more general ones, by correspondingly defining two new classes of Petri net generators: labeled Petri nets with outputs (LPNOs) and adaptive labeled Petri nets (ALPNs). To compare the modeling power of different Petri net generators, the notion of observation equivalence is proposed. ALPNs are shown to be the class of bounded generators possessing the highest modeling power. Looking for bridges between the different formalisms, we first present a general procedure to convert a bounded LPNO into an equivalent ALPN or even into an equivalent labeled Petri net (if any exists). Finally, we discuss the possibility of converting an unbounded LPNO into an equivalent ALPN

Structural computation of alignments of business processes over partial orders

Relating event data and process models is becoming an important element for organizations. This paper presents a novel approach for aligning traces and process models. The approach is based on the structural theory of Petri nets (the marking equation), applied over an unfolding of the initial process model. Given an observed trace, the approach adopts an iterative optimization mechanism on top of the unfolding, computing at each iteration part of the resulting alignment. In contrast to the previous work that is primarily grounded in the marking equation, this approach is guaranteed to provide real solutions, and tries to mimic as much as possible the events observed in the trace. Experiments witness the significance of this approach both in quality and execution time perspectives.Peer ReviewedPostprint (author's final draft

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Fluidization of Petri nets to improve the analysis of Discrete Event Systems

Las Redes de Petri (RdP) son un formalismo ampliamente aceptado para el modelado y análisis de Sistemas de Eventos Discretos (SED). Por ejemplo sistemas de manufactura, de logística, de tráfico, redes informáticas, servicios web, redes de comunicación, procesos bioquímicos, etc. Como otros formalismos, las redes de Petri sufren del problema de la ¿explosión de estados¿, en el cual el número de estados crece explosivamente respecto de la carga del sistema, haciendo intratables algunas técnicas de análisis basadas en la enumeración de estados. La fluidificación de las redes de Petri trata de superar este problema, pasando de las RdP discretas (en las que los disparos de las transiciones y los marcados de los lugares son cantidades enteras no negativas) a las RdP continuas (en las que los disparos de las transiciones, y por lo tanto los marcados se definen en los reales). Las RdP continuas disponen de técnicas de análisis más eficientes que las discretas. Sin embargo, como toda relajación, la fluidificación supone el detrimento de la fidelidad, dando lugar a la pérdida de propiedades cualitativas o cuantitativas de la red de Petri original. El objetivo principal de esta tesis es mejorar el proceso de fluidificación de las RdP, obteniendo un formalismo continuo (o al menos parcialmente) que evite el problema de la explosión de estados, mientras aproxime adecuadamente la RdP discreta. Además, esta tesis considera no solo el proceso de fluidificación sino también el formalismo de las RdP continuas en sí mismo, estudiando la complejidad computacional de comprobar algunas propiedades. En primer lugar, se establecen las diferencias que aparecen entre las RdP discretas y continuas, y se proponen algunas transformaciones sobre la red discreta que mejorarán la red continua resultante. En segundo lugar, se examina el proceso de fluidificación de las RdP autónomas (i.e., sin ninguna interpretación temporal), y se establecen ciertas condiciones bajo las cuales la RdP continua preserva determinadas propiedades cualitativas de la RdP discreta: limitación, ausencia de bloqueos, vivacidad, etc. En tercer lugar, se contribuye al estudio de la decidibilidad y la complejidad computacional de algunas propiedades comunes de la RdP continua autónoma. En cuarto lugar, se considera el proceso de fluidificación de las RdP temporizadas. Se proponen algunas técnicas para preservar ciertas propiedades cuantitativas de las RdP discretas estocásticas por las RdP continuas temporizadas. Por último, se propone un nuevo formalismo, en el cual el disparo de las transiciones se adapta a la carga del sistema, combinando disparos discretos y continuos, dando lugar a las Redes de Petri híbridas adaptativas. Las RdP híbridas adaptativas suponen un marco conceptual para la fluidificación parcial o total de las Redes de Petri, que engloba a las redes de Petri discretas, continuas e híbridas. En general, permite preservar propiedades de la RdP original, evitando el problema de la explosión de estados

Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties