This paper presents and formally defines the CO-OPN/2 formalism (Concurrent Object-Oriented Petri Net) which is devised for the specification of large concurrent systems. We introduce the basic principles of the formalism, and describe how some aspects of object-orientation -- such as the notions of class/object, object reference, inheritance and subtyping -- are taken into account. In CO-OPN/2, classes (considered as templates) are described by means of algebraic nets in which places play the role of attributes, and methods are external parameterized transitions. A semantic extension for the management of the object references is defined. Inheritance and subtyping are clearly distinguished. Interaction between objects consists of synchronizations. Synchronization expressions are provided which allow the designer to select interaction policies between the partners. We also provide a step semantics which expresses the true concurrency of the object behaviors. Finally, in orde...

This paper describes the current status of the verification testbed PEP (Programming Environment based on Petri Nets) from a personal perspective of the author. The paper concentrates on what are perceived as the main highlights and the major shortcomings of PEP.

The aim of this paper is to briefly introduce the Concurrent Object-Oriented Petri Net specification language CO-OPN/2 which has overcome some limitations of its object-based ancestor CO-OPN. Classes are described by means of algebraic nets in which places play the role of attributes, and methods function as external parameterized transitions. Inheritance and sub-typing are distinguished, with the former is considered as a mechanism for reuse while the later is viewed on a semantic level, based on the substitutability principle with respect to the behavior of the objects. As in the CO-OPN language, cooperation between the objects is achieved by means of synchronization expressions which allow the designer to select object interaction policies.

The concept of rule-based modification developed in the area of algebraic graph transformations and high-level replacement systems has recently shown to be a powerful concept for vertical stucturing of Petri nets. This includes low-level and high-level Petri nets, especially algebraic high-level nets which can be considered as an integration of algebraic specifications and Petri nets. In a large case study rule-based modi cation of algebraic high-level nets has been applied successfully for the requirements analysis of a medical information system. The main new result in this paper extends rule-based modification of algebraic high-level nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rule-based modi cation of algebraic high-level nets as a vertical development strategy this extension is an important new technique. It is called rule-based re nement. As a running example an important safety property of a medical information system is considered and is shown to be preserved under rule-based refinement.

. We are interested in the composition of languages, in particular a data description language and a paradigm-specific language, from a pragmatic point of view. Roughly speaking our goal is the description of languages in a component-based style, focussing on the data definition component. The proposed approach is to substitute the constructs dealing with data from the "data" language for the constructs describing data that are not specific to the particular paradigm of the "paradigm-specific" language in a way that syntax, semantics as well as methodologies of the two components are preserved. We illustrate our proposal on a toy example: using the algebraic specification language Casl, as data language, and a "pre-post" condition logic `a la Hoare, as the paradigm specific one. A more interesting application of our technique is fully worked out in [16] and the first step towards an application to UML, that is an analysis of UML from the data viewpoint, following the guid...

this paper, we consider a Petri net semantics for BPEL. The semantics is complete (i.e., covers all the standard and exceptional behaviour of BPEL), and formal (i.e., feasible for model checking). With Petri nets, several elegant technologies such as the theory of workflow nets [vdA98], a theory of controllability [Mar04, Sch04], a long list of verification techniques [Sch00] and tools [RWL 03, SR00, Sch00] become directly applicable. The Petri net semantics provides patterns for each BPEL activity. Compound activities contain slots for the patterns of their subactivities. This way, it is possible to translate BPEL processes automatically into Petri nets. Using high-level Petri nets, data aspects can be fully incorporated while these aspects can as well be ignored by switching to low-level Petri nets

this paper. Multiset-signatures and-algebras In an algebraic system net a token on a place is an element of a domain of some algebra. Then, the multitude of tokens on a particular place can be represented as a multiset. In order to talk about the multitude of tokens one a place within the algebraical framework, we include the multiset over the corresponding sort in the algebra. To this end, we introduce multiset-signatures as particular signatures. For a signature

Algebraic Petri nets as defined by Reisig [15] lack a feature for modelling distributed network algorithms, viz. flexible arcs. In this paper we equip algebraic Petri nets with flexible arcs and we call the resulting extension algebraic system nets. We demonstrate that algebraic system nets are better suited for modelling distributed algorithms. Besides this practical motivation for introducing algebraic system nets there is a theoretical one. The concept of place invariants introduced along with algebraic Petri nets has a slight insufficiency: There may be place invariants of an unfolded algebraic Petri net which cannot be expressed as a place invariant of the algebraic Petri net itself. By introducing algebraic system nets along with a slightly more general concept of place invariants we also eliminate this insufficiency. Moreover, we generalize the concept of place invariants which we call simulations. Many well-known concepts of Petri net theory such as siphons, tra...

. In some phases of system development state-based methods are adequate; in others event-based methods are adequate. Petri nets provide a system model which supports both methods and thus allow a smooth transition between the different phases of system development. Most temporal logics for Petri nets, however, do not support both methods. In this paper we introduce a temporal logic for Petri nets which allows to argue on states as well as on events. This way, specifications in the early phases can be event based and verification in later phases can be state-based within a single formalism. Keywords: Temporal logic; events; states; Petri nets; system development; specification; verification. Introduction Most formal methods employed for the specification and development of distributed systems are either event-based or state-based. The event-based methods highlight the events and their relation; the state-based methods emphasize the states and the state changes. Both approach...

In this article we present the concurrent object-oriented specification language CO-OPN/2 which extends the CO-OPN (Concurrent Object Oriented Petri Nets) formalism, destined to support the specification of large distributed systems. The CO-OPN/2 approach proposes a specification language, based on the object-oriented paradigm, which includes a fine description of true concurrent behavior. This hybrid approach (model and property-oriented) allows for a description of the concurrent aspects through the use of high-level Petri nets which includes data structures expressed as algebraic abstract data types and a synchronization mechanism for building abstraction hierarchies. This latter notion is the concept which is used in application structuring. Some nice properties of CO-OPN/2, such as the progressive refinement of specifications, allow for an incremental building of systems. In this article, we introduce CO-OPN/2 informally, by means of a typical example of distributed system, the tr...