Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.Comment: 35 pages, 5 figure

Profiling the publish/subscribe paradigm for automated analysis using colored Petri nets

UML sequence diagrams are used to graphically describe the message interactions between the objects participating in a certain scenario. Combined fragments extend the basic functionality of UML sequence diagrams with control structures, such as sequences, alternatives, iterations, or parallels. In this paper, we present a UML profile to annotate sequence diagrams with combined fragments to model timed Web services with distributed resources under the publish/subscribe paradigm. This profile is exploited to automatically obtain a representation of the system based on Colored Petri nets using a novel model-to-model (M2M) transformation. This M2M transformation has been specified using QVT and has been integrated in a new add-on extending a state-of-the-art UML modeling tool. Generated Petri nets can be immediately used in well-known Petri net software, such as CPN Tools, to analyze the system behavior. Hence, our model-to-model transformation tool allows for simulating the system and finding design errors in early stages of system development, which enables us to fix them at these early phases and thus potentially saving development costs

On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems

Predictive performance models are used increasingly throughout the phases of the software engineering lifecycle of distributed systems. However, as systems grow in size and complex-ity, building models that accurately capture the different aspects of their behavior becomes a more and more challenging task. The challenge stems from the limited model expressivenes

A hazard analysis via an improved timed colored petri net with time–space coupling safety constraint

AbstractPetri nets are graphical and mathematical tools that are applicable to many systems for modeling, simulation, and analysis. With the emergence of the concept of partitioning in time and space domains proposed in avionics application standard software interface (ARINC 653), it has become difficult to analyze time–space coupling hazards resulting from resource partitioning using classical or advanced Petri nets. In this paper, we propose a time–space coupling safety constraint and an improved timed colored Petri net with imposed time–space coupling safety constraints (TCCP-NET) to fill this requirement gap. Time–space coupling hazard analysis is conducted in three steps: specification modeling, simulation execution, and results analysis. A TCCP-NET is employed to model and analyze integrated modular avionics (IMA), a real-time, safety-critical system. The analysis results are used to verify whether there exist time–space coupling hazards at runtime. The method we propose demonstrates superior modeling of safety-critical real-time systems as it can specify resource allocations in both time and space domains. TCCP-NETs can effectively detect underlying time–space coupling hazards

Simplifying the verification of simulation models through Petri net to FlexSim mapping

Simplifying the encoding of a simulation conceptual model representation reduces the number of errors that will be detected in the verification phase. In this paper, we present a mapping between Petri nets, a well-known formalism, and FlexSim, a well-known simulation tool. The proposal is illustrated through an example of how a model specified in a Petri net can be encoded easily, reducing the time needed to understand and verify the model. In the proposed methodology, the mapping must be defined at the initial stage of the encoding, starting from (in this case) a Petri net conceptual model, and ending at the encoding tool (FlexSim in this case). The main advantages of the proposed methodology are discussed.Peer ReviewedPostprint (author's final draft

Using Colored Stochastic Petri Net (CS-PN) software for protocol specification, validation, and evaluation

The specification, verification, validation, and evaluation, which make up the different steps of the CS-PN software are outlined. The colored stochastic Petri net software is applied to a Wound/Wait protocol decomposable into two principal modules: request or couple (transaction, granule) treatment module and wound treatment module. Each module is specified, verified, validated, and then evaluated separately, to deduce a verification, validation and evaluation of the complete protocol. The colored stochastic Petri nets tool is shown to be a natural extension of the stochastic tool, adapted to distributed systems and protocols, because the color conveniently takes into account the numerous sites, transactions, granules and messages