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Results on refinements of places and transitions in Petri nets are surveyed. Such refinements may either transform a net to a refined net with the same behaviour, where behaviour often means safeness or liveness. Or they may transform semantically equivalent nets to refined nets which are semantically equivalent again. Here the semantics of a net is a description of the possible runs incorporating...
This paper describes a distributed simulator of high order Petri nets for a parallel computer. It shows how the inherent parallelism of a Petri net can be used to obtain a fast simulator. The design decisions made in implementing a distributed simulator in hardware and software are discussed and a detailed description of both is given. The simulator is a component of a suite of tools which...
After having described the importance and the complexity of monitoring Flexible Manufacturing Systems, this paper shows the interest of introducing uncertainty and imprecision within Petri net based models. These two concepts are then introduced through a modification of the marking of a Petri net with Objects, and of its interpretation (external conditions associated with the transitions). It is...
P-semiflows are non-negative left anullers of a net's flow matrix. The importance of these vectors lies in their usefulness for analyzing net properties. The concept of minimal p-semiflow is known in the context of Mathematical Programming under the name "extremal direction of a cone". This connection highlights a parallelism between properties found in the domains of P/T nets and Mathematical...
The state equation is a linear description of the reachable markings and firing count vectors of a P/T net. It has the disadvantage that its solution space, in general, includes additional integer unreachable or/and unfirable vectors. As a result, the analysis of properties using this linear characterization, usually leads to necessary or sufficient conditions for satisfying it, but not both. The...
Commutative nets are a subclass of colored nets whose color functions belong to a ring of commutative diagonalizable endomorphisms. Although their ability to describe models is smaller than that of colored nets, they can handle a broad range of concurrent systems. Commutative nets include net subclasses such as regular homogeneous nets and ordered nets, whose practical importance has already been...
Vicinity respecting net morphisms are a restricted class of net morphisms. The restriction requires that pre- and post-sets of elements are respected by the morphisms. However, vicinity respecting net morphisms allow to map S-elements to T-elements and vice versa and can hence formalize contractions of nets. Amongst some general properties of net morphisms and in particular of vicinity respecting...
An extension of regular nets, a class of colored nets, to a stochastic model is proposed. We show that the symmetries in this class of nets make it possible to develop a performance evaluation by constructing only a graph of symbolic markings, which vertices are classes of states, instead of the whole reachability graph. Using algebraic techniques, we prove that all the states in a class have the...
This paper introduces two new structural objects for the study of nets: handles and bridges. They are shown to provide sufficient, although not necessary, conditions of good behaviour for general ordinary nets, as well as a new characterisation of structural liveness and structural boundedness for the subclass of Free Choice nets. This characterisation is used to approach a modular synthesis theory...
This invited paper present in a semi-formal illustrative way several new results concerning the analysis and synthesis of free choice systems. It is a complementary work of the survey by E. Best [Best 87]. In the analysis part, we characterize liveness and boundedness in linear algebraic terms. As a consequence of the new characterizations, both properties are shown to be decidable (as a whole) in...
This paper is devoted to the performance analysis of an election protocol for a unidirectional ring proposed by C.Kaiser. We give two models of increasing complexity in order to compute several performance criteria. The two models (called initiation model and evaluation model) are defined using coloured Petri nets. For these models several qualitative properties are proven. Then the required performance...
The paper shows how to extend Coloured Petri Nets with a hierarchy concept. The paper proposes five different hierarchy constructs, which allow the analyst to structure large CP-nets as a set of interrelated subnets (called pages). The paper discusses the properties of the proposed hierarchy constructs, and it illustrates them by means of two examples. The hierarchy constructs can be used for theoretical...
This paper describes how Coloured Petri Nets (CP-nets) have been developed — from being a promising theoretical model to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or computers communicate by means of some more or less formal rules). First CP-nets are introduced...
The paper describes a distributed modeling system architecture, designed to support various graph models of computation, including predicate/transition nets and colored Petri nets. To demonstrate the utility of the architecture, we describe an implementation for a specific graph model (one that is related to, but distinct from, Petri nets). The architecture provides for interactive editing and interpretation...
The paper introduces a notion of preorder between Elementary Net Systems which is based on the observability of places. This latter allows one to define the notion of Observable Local States whose transformations are the main concern of the proposed preorder, called State Transformation (ST) preorder. ST preorder compares systems with a different level of granularity in local states transformation...
The general idea of this paper is to build a system in a modular way and to deduce its properties only by analysing its smaller components. Since, in general, composing subnets does not preserve properties (especially liveness) at the level of the global net, the problem is to find constraints on the subnets for establishing such results. We have discovered that in some cases it is sufficient to put...
We have developed a new model of hypertext in pilot studies. The traditional hypertext model resembles a directed graph, representing information fragments and the relationships that tie the fragments together. Our model, based on Petri nets, also represents the hypertext's browsing semantics (i.e., how the information is to be visited). The Petri net model is a generalization of traditional directed...
The “stubborn set” theory and method for generating reduced state spaces is presented. The theory takes advantage of concurrency, or more generally, of the lack of interaction between transitions, captured by the notion of stubborn sets. The basic method preserves all terminal states and the existence of nontermination. A more advanced version suited to the analysis of properties of reactive systems...
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