Andrzej M. Borzyszkowski

General Morphisms of Petri Nets (Extended Abstract)

A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of Petri nets is shown to admit products. Potential applications of general morphisms are indicated.

On Concurrent Realization of Reactive Systems and Their Morphisms

The paper introduces the notion of concurrent realization of reactive systems. A framework is also presented in which labelled safe Petri nets as concurrent realizations of concrete asynchronous systems are constructed. The construction is uniform in the sense that it extends to a realization of arbitrary commuting diagrams. We discuss applicability of the framework to construct maximally concurrent realizations of reactive systems.

Finite Completeness of Categories of Petri Nets

The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some well-known categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete.

Transition systems without transitions

We study the problem of embedding partial 2-structures into set 2-structures such that the target structure is full and forward closed and it is minimal w.r.t, these properties.Ehrenfeucht and Rozenberg introduced the notion of partial 2-structures--an abstract form of transition systems--and studied the problem of representing them as partial set 2-structures--directed graphs made of sets and their ordered symmetric differences. They constructed a representation and gave the conditions under which the representation is an isomorphism.We propose an alternative representation of partial 2-structures by partial set 2-structures which are complete graphs, hence their transitions may be left implicit, yielding a static representation of dynamic systems.

CPO's do not form a CPO, and yet Recursion Works

We consider type universes as examples of regular algebras in the area of the denotational semantics of programming languages. The paper concentrates on our method which was used implicitly in the studies of the domain universes underlying MetaSoft, cf. [BBP90], and BSI/VDM, cf. [TW90].

Understanding an informal Description: Office Documents Architecture, an ISO Standard

Introduction This report has come to being while we were reading the Draft ISO Standard 8613, Parts 1-6: OOce Documents Architecture and interchange format ODA]. The precise nature of that undertaking may be of no concern for the Reader but we think it is typical of many projects arising in an industrial environment, and as such it may serve to illustrate some ways of lling the gap between the VDM theory and the industrial practice. ODA is a large project seeking to fullll connicting demands of many partners. We believe many discussions and negotiations must have preceded setting up the nal document. Without taking part in these activities ODA] is rather diicult to understand. The authors of ODA apparently lacked means to communicate ideas: the description suuers from many ambiguities, loopholes, imprecise statements and unstructured presentation. Some of these drawbacks could have been easily prevented or at least detected had they decided in the rst place to use VDM in one or another available version. Although ODA is not a software project it may be conveniently viewed as a kind of a language, and VDM techniques may be applied where they seem unapplicable at rst sight. We hope that using the well-established VDM methods in an unorthodox eld may prove interesting to the VDM community. We have tried to formalize ODA in the MetaSoft dialect of the VDM. The diierences between MetaSoft and the other lines of VDM are not as far reaching as to require explanations for understanding this report, so just do not worry about them. In emergency respective references are BJ] for VDM and Bli] for MetaSoft. The notations appearing in this report are summarized in Section 1. In our formalization attempt we have gone as far as could have been safely done on the basis of the existing written documentation of ODA. Credits for this research are due to Andrzej Blikle, a coauthor of BSB], upon which the current report is based, for his contribution and his encouragement.