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

On the Enforcement of a Class of Nonlinear Constraints on Petri Nets

International audienceThis paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunc-tive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach

On Petri Nets with Hierarchical Special Arcs

We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy of places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also investigate what happens when we have a mix of these special arcs, some of which respect the hierarchy, while others do not. We settle the decidability status of the above four problems for all combinations of hierarchy, inhibitor, reset and transfer arcs, except the termination problem for two combinations. For both these combinations, we show that deciding termination is as hard as deciding the positivity problem on linear recurrence sequences -- a long-standing open problem

Model interoperability via model driven development

It is widely recognised that software development is a complex process. Among the factors that contribute to its inherent complexity is the gap between the design and the formal analysis domains. Software design is often considered a human oriented task while the analysis phase draws on formal representation and mathematical foundations. An example of this dichotomy is the use of UML for the software design phase and Petri Nets for the analysis; a separation of concerns that leads to the creation of heterogeneous models. Although UML is widely accepted as a language that can be used to model the structural and behavioural aspects of a system, its lack of mathematical foundations is seen as a serious impediment to rigorous analysis. Petri Nets on the other hand have a strong mathematical basis that is well suited for formal analysis; they lack however the appeal and the easeof-use of UML. A pressing concern for software developers is how to bridge the gap between these domains and allow for model interoperability and the integration of different toolsets across them, and thus reduce the complexity of the software development process. The aim of this paper is to present a Model Driven Development (MDD) model transformation which supports a seamless transition between UML and Petri Nets. This is achieved by model interoperability between UML Sequenc

Towards verification of computation orchestration

Recently, a promising programming model called Orc has been proposed to support a structured way of orchestrating distributed Web Services. Orc is intuitive because it offers concise constructors to manage concurrent communication, time-outs, priorities, failure of Web Services or communication and so forth. The semantics of Orc is precisely defined. However, there is no automatic verification tool available to verify critical properties against Orc programs. Our goal is to verify the orchestration programs (written in Orc language) which invoke web services to achieve certain goals. To investigate this problem and build useful tools, we explore in two directions. Firstly, we define a Timed Automata semantics for the Orc language, which we prove is semantically equivalent to the operational semantics of Orc. Consequently, Timed Automata models are systematically constructed from Orc programs. The practical implication is that existing tool supports for Timed Automata, e.g., Uppaal, can be used to simulate and model check Orc programs. An experimental tool has been implemented to automate this approach. Secondly, we start with encoding the operational semantics of Orc language in Constraint Logic Programming (CLP), which allows a systematic translation from Orc to CLP. Powerful constraint solvers like CLP(R) are then used to prove traditional safety properties and beyond, e.g., reachability, deadlock-freeness, lower or upper bound of a time interval, etc. Counterexamples are generated when properties are not satisfied. Furthermore, the stepwise execution traces can be automatically generated as the simulation steps. The two different approaches give an insight into the verification problem of Web Service orchestration. The Timed Automata approach has its merits in visualized simulation and efficient verification supported by the well developed tools. On the other hand, the CPL approach gives better expressiveness in both modeling and verification. The two approaches complement each other, which gives a complete solution for the simulation and verification of Computation Orchestration