A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes

We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published in the the Proceedings of TACAS 2007, LNCS 442

An Operational Petri Net Semantics for the Join-Calculus

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this gap by providing an abstract specification language which is asynchronously distributable. Classical process semantics establish an implicit order of actually independent actions, by means of an interleaving. So does the semantics of the join-calculus. To capture such independent actions, step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri net semantics for the join-calculus induces step-behavior in a natural way. We prove our semantics behaviorally equivalent to the original join-calculus semantics by means of a bisimulation. We discuss how join specific assumptions influence an existing notion of distributability based on Petri nets.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Petri Nets and Other Models of Concurrency

This paper retraces, collects, and summarises contributions of the authors --- in collaboration with others --- on the theme of Petri nets and their categorical relationships to other models of concurrency

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

Design Environments for Complex Systems

The paper describes an approach for modeling complex systems by hiding as much formal details as possible from the user, still allowing verification and simulation of the model. The interface is based on UML to make the environment available to the largest audience. To carry out analysis, verification and simulation we automatically extract process algebras specifications from UML models. The results of the analysis is then reflected back in the UML model by annotating diagrams. The formal model includes stochastic information to handle quantitative parameters. We present here the stochastic -calculus and we discuss the implementation of its probabilistic support that allows simulation of processes. We exploit the benefits of our approach in two applicative domains: global computing and systems biology

A Simulation Model Articulation of the REA Ontology

This paper demonstrates how the REA enterprise ontology can be used to construct simulation models for business processes, value chains and collaboration spaces in supply chains. These models support various high-level and operational management simulation applications, e.g. the analysis of enterprise sustainability and day-to-day planning. First, the basic constructs of the REA ontology and the ExSpect modelling language for simulation are introduced. Second, collaboration space, value chain and business process models and their conceptual dependencies are shown, using the ExSpect language. Third, an exhibit demonstrates the use of value chain models in predicting the financial performance of an enterprise

Towards a Notion of Distributed Time for Petri Nets

We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks --- possibly one per place --- allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models