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

Isotactics as a foundation for alignment and abstraction of behavioral models

There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions

Consistency in Multi-Viewpoint Architectural Design of Enterprise Information Systems

Different stakeholders in the design of an enterprise information system have their own view on that design. To help produce a coherent design this paper presents a framework that aids in specifying relations between such views. To help produce a consistent design the framework also aids in specifying consistency rules that apply to the view relations and in checking the consistency according to those rules. The framework focuses on the higher levels of abstraction in a design, we refer to design at those levels of abstraction as architectural design. The highest level of abstraction that we consider is that of business process design and the lowest level is that of software component design. The contribution of our framework is that it provides a collection of basic concepts that is common to viewpoints in the area of enterprise information systems. These basic concepts aid in relating viewpoints by providing: (i) a common terminology that helps stakeholders to understand each others concepts; and (ii) a basis for defining re-usable consistency rules. In particular we define re-usable rules to check consistency between behavioural views that overlap or are a refinement of each other. We also present an architecture for a tool suite that supports our framework. We show that our framework can be applied, by performing a case study in which we specify the relations and consistency rules between the RM-ODP enterprise, computational and information viewpoints

Semantic Embedding of Petri Nets into Event-B

We present an embedding of Petri nets into B abstract systems. The embedding is achieved by translating both the static structure (modelling aspect) and the evolution semantics of Petri nets. The static structure of a Petri-net is captured within a B abstract system through a graph structure. This abstract system is then included in another abstract system which captures the evolution semantics of Petri-nets. The evolution semantics results in some B events depending on the chosen policies: basic nets or high level Petri nets. The current embedding enables one to use conjointly Petri nets and Event-B in the same system development, but at different steps and for various analysis.Comment: 16 pages, 3 figure

Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation

Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. The abstraction theory therefore provides a mechanism for coping with the state space explosion problem and supports the analysis and comparison of multi-valued networks. We take as our starting point the abstraction theory for synchronous multi-valued networks which is based on the finite set of traces that represent the behaviour of such a model. The problem with extending this approach to the asynchronous case is that we can now have an infinite set of traces associated with a model making a simple trace inclusion test infeasible. To address this we develop a decision procedure for checking asynchronous abstractions based on using the finite state graph of an asynchronous multi-valued network to reason about its trace semantics. We illustrate the abstraction techniques developed by considering a detailed case study based on a multi-valued network model of the regulation of tryptophan biosynthesis in Escherichia coli.Comment: Presented at MeCBIC 201

Petri nets with may/must semantics: Preserving properties through data refinements

Many systems used in process managements, like workflow systems, are developed in a top-down fashion, when the original design is refined at each step bringing it closer to the underlying reality. Underdefined specifications cannot however be used for verification, since both false positives and false negatives can be reported. In this paper we introduce colored Petri nets where guards can be evaluated to true, false and indefinite values, the last ones reflecting underspecification. This results in the semantics of Petri nets with may- and must-enableness and firings. In this framework we introduce property-preserving refinements that allow for verification in an early design phase. We present results on property preservation through refinements. We also apply our framework to workflow nets, introduce notions of may- and must-soundness and show that they are preserved through refinements. We shortly describe a prototype under implementation

Higher Dimensional Transition Systems

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures