Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page

Graph Creation, Visualisation and Transformation

We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting

A categorical framework for concurrent, anticipatory systems

A categorical semantic domain is constructed for Petri nets which satisfies the diagonal compositionality requirement with respect to anticipations, i.e., Petri nets are equipped with a compositional anticipation mechanism (vertical compositionality) that distributes through net combinators (horizontal compositionality). The anticipation mechanism is based on graph transformations (single pushout approach). A finitely bicomplete category of partial Petri nets and partial morphisms is introduced. Classes of transformations stand for anticipations. The composition of anticipations (i.e., composition of pushouts) is defined, leading to a category of nets and anticipations which is also complete and cocomplete. Since the anticipation operation composes, the vertical compositionality requirement of Petri nets is achieved. Then, it is proven that the anticipation also satisfies the horizontal compositionality requirement. A specification grammar stands for a system specification and the corresponding induced subcategory of nets and anticipation's stands for ali possible dynamic anticipation's ofthe system (objects) and their relationship (morphims)

Requirements Specification for Controller Design-from Use Cases to IOPT Net Models

12th IEEE International Conference on Industrial Informatics, INDIN , Porto Alegre: Jul 27-30, 2014Non-autonomous Petri nets offer a language especially adapted for controller specifications. They are typically used in the design phase often with no clear connection to the analysis phase, including requirements specification. This paper shows how use cases can be used to support requirements specification amenable to a direct transformation to IOPT nets, a class of non-autonomous Petri nets. To that end, we propose a set of semi-formal rules for use case descriptions, including use case relationships, which take advantage of the concepts available in IOPT nets, namely input and output signals and events and net addition, a net composition operation

Conflict Equivalence of Branching Processes

International audienceFor concurrent and large systems, specification step is a crucial point. Combinatory explosion is a limit that can be encountered when a state space exploration is driven on large specification modeled with Petri nets. Considering bounded Petri nets, technics like unfolding can be a way to cope with this problem. This paper is a first attempt to present an axiomatic model to produce the set of processes of unfoldings into a canonic form. This canonic form allows to define a conflict equivalence

Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201

Multi-robot Motion Planning based on Nets-within-Nets Modeling and Simulation

This paper focuses on designing motion plans for a heterogeneous team of robots that has to cooperate in fulfilling a global mission. The robots move in an environment containing some regions of interest, and the specification for the whole team can include avoidances, visits, or sequencing when entering these regions of interest. The specification is expressed in terms of a Petri net corresponding to an automaton, while each robot is also modeled by a state machine Petri net. With respect to existing solutions for related problems, the current work brings the following contributions. First, we propose a novel model, denoted {High-Level robot team Petri Net (HLPN) system, for incorporating the specification and the robot models into the Nets-within-Nets paradigm. A guard function, named Global Enabling Function (gef), is designed to synchronize the firing of transitions such that the robot motions do not violate the specification. Then, the solution is found by simulating the HPLN system in a specific software tool that accommodates Nets-within-Nets. An illustrative example based on a Linear Temporal Logic (LTL) mission is described throughout the paper, complementing the proposed rationale of the framework.Comment: submitted to 62nd IEEE Conference on Decision and Control, Dec. 13-15, 202

Augmenting High-Level Petri Nets to Support GALS Distributed Embedded Systems Specification

Part 9: Embedded Systems and Petri NetsInternational audienceHigh-level Petri net classes are suited to specify concurrent processes with emphasis both in control and data processing, making them appropriate to specify distributed embedded systems (DES). Embedded systems components are usually synchronous, which means that DES can be seen as Globally-Asynchronous Locally-Synchronous (GALS) systems. This paper proposes to include in high-level Petri nets a set of concepts already introduced for low-level Petri nets allowing the specification of GALS systems, namely time domains, test arcs and priorities. Additionally, this paper proposes external messages and three types of (high-level) asynchronous communication channels, to specify the interaction between distributed components based on message exchange. With these extensions, GALS-DES can be specified using high-level Petri nets. The resulting models include the specification of each component with well-defined boundaries and interface, and also the explicit specification of the asynchronous interaction between components. These models will be used not only to specify the system behavior, but also to be the input for model-checking tools (supporting its verification) and automatic code generation tools (supporting its implementation in software and hardware platforms), giving a contribution to the model-based development approach and hardware-software co-design of DES based on high-level Petri nets

Space upper bound analysis for transformation from elementary reference-net system to low-level P/T nets

Elementary Reference-nett Systems (ERS) is a class of Object-Oriented Petri Nets that follows the nets-within-nets paradigm. It combines theoretical properties as well as numerous practical needs for multi-agent-systems specification. However, it comes with some constraints that limit their expressiveness for automatic verification purposes due to the highly expressive nature of the underlying class of Petri nets. This article presents a set of transformation procedure from ERS to basic Petri nets in order to make verification feasible. It further establishes the space upper bound for the transformation which shows that the state space of the transformed P/T net grows exponentially as the number of object nets increases.Keywords: Petri nets, object orientation, agent systems, interaction, mobility, transformatio