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The desire to replace conventional forms of cooperation within organizational structures by computer services raises the necessity to model cooperation and to describe it formally. The complexity inherent to cooperating systems calls for a carefully structured design facilitating their analysis as well as their implementation and test. In this paper we describe an example from the area...
In order to make easier the verification of parallel systems, we present a set of transformations which preserve several classical properties of nets: boundednes, safety, covering by S-invariants, proper termination, home states, unavoidable states, liveness and abstraction. These transformations are powerful enough to construct all other transformations defined before. We conclude with examples of...
We show that, as transition systems, Petri nets may be expressed by terms of a calculus of processes which is a variant of Milner's SCCS. We then prove that the class of labelled nets forms a subcalculus, thus an algebra, with juxtaposition, adding condition and labelling as primitive operations. Finally we introduce rational machines which express explicit synchronizations on nets.
The paper is based on the consideration of controls by restrictions of behaviour as introduced in [Bu]. Different notions of fairness and fair controls are derived from the fairness notions given in [LPS]: fairness is considered with or without reference to the behaviour of the original uncontrolled system, in connection with deadlock-avoidance (infinite fair controls) and by omitting termination...
In this paper the definitions of process of a C/E system given in the literature are carefully analyzed and discussed on the basis of some examples. Then, a new definition of process is developed, resulting in alpha- and beta-processes. These (beta) processes are investigated and turn out to have "less disadvantages" than the original processes.
Synchronic distances are system invariants representing fundamental system properties. There is a strong connection between synchronic distances and concurrency, but as we can see from this paper that such distances are a mixed measure of both concurrent and sequential phenomena. This paper devotes to the investigation of the meaning of synchronic distance values, while a measure of sequential behaviour,...
It is a common practice in system design to build a system from its given behaviour. It is the general purpose in system analysis to get to know system behaviour from its structure. A common problem in both the two areas is how to specify. or to represent. system behaviour? This paper propose PROCESS PERIOD as the basic means of describing system behaviour, provided Petri Nets are used to model the...
First steps towards methods really applicable to deal with large specifications of real-life systems are offered in this paper. Specifically, Petri-net methods are applied to specifications written in CCITT's Specification and Description Language. As an example, the Telephone User Part of the CCITT n.7 system is discussed. By means of restriction of concerns, analysis is performed on...
In this paper, we have given different elementary illustrative examples of modelling flexible production by means of AP-nets. This method enables connections and deconnections of subgraphs to be easily represented which is not possible by the use of priority nets or by nets with inhibitors edges. Moreover AP-nets are also suitable for modelling priority, and communications between the operative part,...
Nets considered here are "abstract" since their places are seen as individual variables, transitions as function names and a firing rule as a predicate stating when a partial function, denoted by a given transition, is defined. Three selected rules expressing the local character of transition's activity are admitted as axioms for interpretation. The nets are "structured" because...
This paper reflects on the application of nets in system description, analysis and design and the role of tools herein. General tool requirements are given with respect to structure, user interface and functionality. Moreover general applicability of tools and inter-tool communication are highlighted. In an appendix an overview of currently available net-based tools is given.
A simple formalism for omitting details of CE-systems called projection is presented. Projections work with the PrT-net representation of CE-systems and allow to look at a CE-system from a partially quantitative point of view. They provide an unified approach to ordinary PT-nets and to PrT-nets avoiding multisets in the beginning. Their main use is for eliminating individual variables that occur in...
The paper deals with representations of the safe states set in the Banker's problem. Using a Petri Net model we derive formulas for this set (SAFE) directly and for its (smaller) minimal elements set MIN. Moreover, we partition the set MIN into subclasses, so that two elements of the same subclass only differ by the permutation of their components. The set SORT, which contains only one representend...
This paper introduces a new approach to Petri net interpretation. With this approach, properly interpreted Petri nets yield new insights about the mechanics of human work organizations. Furthermore, these insights take technically useful form. In the last few years, the approach has led to the development of an industrial software technology — Coordination technology — for the...
This paper describes the formal semantics of a subset of PASCAL, by means of a semantic model based on a combination of denotational semantics and high-level Petri nets. It is our intention that the paper can be used as part of the written material for an introductory course in computer science.
In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in...
For languages recognized by finite automata we have two formalisms at our disposal: regular expressions (Kleene [3]) and logical formulas (Büchi [2]). In the case of Petri net languages there is no formalism like regular expressions. We give here a Büchi-like theorem which characterizes Petri net languages in terms of second order logical formulas. This characterization situates exactly the...
The co-relation of a partially ordered set (poset) holds true between a and b iff neither a<b nor b<a. Since the co-relation does not change if we proceed to the dual poset, the co-relation determines the order relation at most up to duality. This remark leads us to the idea of "natural order": A poset is called a natural order iff the order relation is determined uniquely up to duality...
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