Catalytic and communicating Petri nets are Turing complete

In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete

Design of testbed and emulation tools

The research summarized was concerned with the design of testbed and emulation tools suitable to assist in projecting, with reasonable accuracy, the expected performance of highly concurrent computing systems on large, complete applications. Such testbed and emulation tools are intended for the eventual use of those exploring new concurrent system architectures and organizations, either as users or as designers of such systems. While a range of alternatives was considered, a software based set of hierarchical tools was chosen to provide maximum flexibility, to ease in moving to new computers as technology improves and to take advantage of the inherent reliability and availability of commercially available computing systems

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

Unfolding Shape Graphs

Shape graphs have been introduced in [Ren04a, Ren04b] as an abstraction to be used in model checking object oriented software, where states of the system are represented as graphs. Intuitively, the graphs modeling the states represent the structure of objects dynamically allocated in the heap. State transitions are then generated by applying graph transformation rules corresponding to the statements of the program. Since the state space of such systems is potentially unbounded, the graphs representing the states are abstracted by shape graphs. Graph transformation systems may be analyzed [BCK01, BK02] by constructing finite structures that approximate their behaviour with arbitrary accuracy, by using techniques developed in the context of Petri nets. The approach of [BK02] is to construct a chain of finite under-approximations of the Winskel’s style unfolding of a graph grammar, as well as a chain of finite over-approximations of the unfolding, where both chains converge to the full unfolding. The approximations may then be used to check properties of the underlying graph transformation system. We apply this technique to approximate the behaviour of systems represented by shape graphs and graph tranformation rules

A review of information flow diagrammatic models for product-service systems

A product-service system (PSS) is a combination of products and services to create value for both customers and manufacturers. Modelling a PSS based on function orientation offers a useful way to distinguish system inputs and outputs with regards to how data are consumed and information is used, i.e. information flow. This article presents a review of diagrammatic information flow tools, which are designed to describe a system through its functions. The origin, concept and applications of these tools are investigated, followed by an analysis of information flow modelling with regards to key PSS properties. A case study of selection laser melting technology implemented as PSS will then be used to show the application of information flow modelling for PSS design. A discussion based on the usefulness of the tools in modelling the key elements of PSS and possible future research directions are also presented

Software Design Modelling with Functional Petri Nets

Petri Nets use two basic primitives: events and conditions to view or model a system. Events are the actions that take place in the system. The occurrence of events is controlled by the "state" of the system, which can be described as a set of conditions. An immediate application of such a model is in the control structures of conventional programming languages. Control structures are the backbone of every programming language. In this paper, an equivalent functional Petri Net (FPN) model is developed for each of the three constructs of structured programs and a FPN Software prototype proposed for the conventional programming construct: if-then-else statement. The motivating idea is essentially to show that FPNs could be used as an alternative approach for program design

Zero-Safe Nets, or Transition Synchronization Made Simple

Abstract In addition to ordinary places, called stable, zero-safe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic when seen from stable places: no stable token generated in a transaction can be reused in the same transaction. Every zero-safe net has an ordinary Place-Transition net as its abstract counterpart, where only stable places are maintained, and where every transaction becomes a transition. The two nets allow us to look at the same system from both an abstract and a refined viewpoint. To achieve this result no new interaction mechanism is used, besides the ordinary token-pushing rules of nets. The refined zero-safe nets can be much smaller than their corresponding abstract P/T nets, since they take advantage of a transition synchronization mechanism. For instance, when transactions of unlimited length are possible in a zero safe net, the abstract net becomes infinite, even if the refined net is finite. In the second part of the paper two universal constructions - both following the Petri nets are monoids approach and the collective token philosophy - are used to give evidence of the naturality of our definitions. More precisely, the operational semantics of zero-safe nets is characterized as an adjunction, and the derivation of abstract P/T nets as a coreflection

Responsible Composition and Optimization of Integration Processes under Correctness Preserving Guarantees

Enterprise Application Integration deals with the problem of connecting heterogeneous applications, and is the centerpiece of current on-premise, cloud and device integration scenarios. For integration scenarios, structurally correct composition of patterns into processes and improvements of integration processes are crucial. In order to achieve this, we formalize compositions of integration patterns based on their characteristics, and describe optimization strategies that help to reduce the model complexity, and improve the process execution efficiency using design time techniques. Using the formalism of timed DB-nets - a refinement of Petri nets - we model integration logic features such as control- and data flow, transactional data storage, compensation and exception handling, and time aspects that are present in reoccurring solutions as separate integration patterns. We then propose a realization of optimization strategies using graph rewriting, and prove that the optimizations we consider preserve both structural and functional correctness. We evaluate the improvements on a real-world catalog of pattern compositions, containing over 900 integration processes, and illustrate the correctness properties in case studies based on two of these processes.Comment: 37 page