Dynamics and steady state analysis of controlled Generalized Batches Petri Nets

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.

The subject of this paper is the legal firing sequence problem (LFS) of Petri nets: given a Petri net PN, an initial marking M and a firing count vector X, find a firing sequence S which starts from M and each transition t appears in /spl delta/ exactly X(t) times as prescribed by X. The results are as follows: (1) LFS is NP-complete even if PN has state machine structure with exactly two kinds of edge weights and X(t)=1 for every transition t; (2) linear time algorithms solving LFS are proposed for several classes of Petri nets having state machine structure.

A new heuristic search approach for scheduling two classes of flexible manufacturing systems (FMSs) that contains assembly operations is proposed. The FMSs are modeled by two classes of Petri nets, called generalized symmetric and asymmetric nets. In the paper, the problem of minimizing makespan is transformed into searching the reachability graph for the optimal (minimal time) firing sequence from the initial marking (state) to the goal marking. A solution of the state equation constitutes a part of the heuristic function. The dynamic information of the nets, such as concurrency and synchronization, is used to adjust the heuristic function since the solution of the state equation may over-estimate the real cost.

In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, S-graphs, algebraic high-level nets, and predicate/transitions nets are instantiations of abstract Petri nets. Moreover, we discuss coloured Petri nets in this context.KeywordsPredicate LogicForgetful FunctorUniform ApproachSpeci CationSignature Morphism

Generic Petri net models of protocol mechanisms in communication systems

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

Petri nets are used as models of asynchronous concurrent systems. The underlying structure of a Petri net is a bipartite digraph. Many properties of Petri nets and the systems they model can be described in graph theoretic terms. These include the notions of deadlocks and traps. In this paper we consider these properties by restricting attention to some special classes of Petri nets including simple, complete, and free-choice Petri nets.

Symmetric and Asymmetric Asynchronous Interaction

Petri nets have been widely used in the design of embedded controllers, namely in electronic hardware and computing platforms design, as well as within automation application areas. This paper presents updated characteristics of one class of Petri nets, named Input-Output Place-Transition Petri nets (IOPT nets), extended to support networked embedded controllers design and globally-asynchronous locally-synchronous (GALS) systems modeling, together with its associated metamodel and execution semantics. The proposed meta-model is compliant with the Petri Net Markup Language (PNML) metamodel, augmented with the descriptions for inputs and outputs, as well as for time domains and communication channels. The meta-model is described using UML class diagrams and has an equivalent Ecore meta-model that positioning IOPT nets within the Eclipse Modeling Framework (EMF).

In this paper, a method is developed to derive the acceptable ranges of objective values for a multi-objective linear fractional programming problem(MOLFPP) with fuzzy parameters both in objectives and constraints. \(\alpha \)- and \(\beta \)-cuts are respectively used in the objectives and constraints to specify the degrees of satisfaction and transform the fuzzy parameters into closed intervals. Using variable transformation and Taylor series expansion, the interval-valued fractional objectives are approximated by intervals of linear functions. The objective functions are assigned proper weights using analytic hierarchy process. Weighting sum method is used to transform the interval-valued multiple objectives into single objective. MOLFPP in interval-valued form is equivalently formulated as two linear problems which derive the acceptable ranges of objective values. Two numerical examples are illustrated to demonstrate the proposed method.

This paper proposes an algorithm to generate the state space of Globally-Asynchronous-Locally-Synchronous (GALS) systems specified with a non-autonomous class of Petri nets. The Input-Output Place-Transition (IOPT) Petri net class is targeted to model automation and embedded systems. It extends the Place-Transition net class with non-autonomous features. To allow GALS systems specification with the IOPT Petri net class, Asynchronous-Channels are used to represent GALS components communication. As GALS systems tend to have large state spaces, a compilation strategy is used in order to improve generation performance. The presented algorithm is implemented in a C program through XSL transformations from the PNML file containing the IOPT net models of the GALS systems, which is then used to generate the intended state space and to identify a set of properties. After the state space analysis, the VHDL code of GALS components is automatically generated from the IOPT net specification, and implemented in FPGA based platforms.

The concept of siphons plays an important role in the analysis of Petri nets. In particular, criteria for liveness and reachability of some subclasses of Petri nets can be stated in terms of siphons. However, the computation of these structural components can be time consuming or even impossible. Recently, a variety of deadlock control policies that rely on partial siphon computation and enumeration have been developed. We propose a polynomial algorithm to find a set of elementary siphons in a class of Petri nets called systems of simple sequential processes with resources, S/sup 3/PR for short. Based on them, other siphons, called dependent ones, can be composed by simple set operations. Case studies show that the proposed algorithm is more computationally efficient than INA, integrated net analyzer, a widely used Petri net analysis tool.

more constraints or equations, with either a linear or nonlinear objective function. This distinction is made primarily on the basis of the difficulty of solving these two types of nonlinear problems. The first type is the less difficult of the two, and in this, Part I of the paper, it is shown how it is solved by the gradient projection method. It should be noted that since a linear objective function is a special case of a nonlinear objective function, the gradient projection method will also solve a linear programming problem. In Part II of the paper [16], the extension of the gradient projection method to the more difficult problem of nonlinear constraints and equations will be described. The basic paper on linear programming is the paper by Dantzig [5] in which the simplex method for solving the linear programming problem is presented. The nonlinear programming problem is formulated and a necessary and sufficient condition for a constrained maximum is given in terms of an equivalent saddle value problem in the paper by Kuhn and Tucker [10]. Further developments motivated by this paper, including a computational procedure, have been published recently [1]. The gradient projection method was originally presented to the American Mathematical Society

Petri nets provide a unifying and versatile framework for the synthesis and engineering of computational models of biochemical reaction networks and of gene regulatory networks. Starting with the basic definitions, we provide an introduction into the different classes of Petri nets that reinterpret a Petri net graph as a qualitative, stochastic, continuous, or hybrid model. Static and dynamic analysis in addition to simulative model checking provide a rich choice of methods for the analysis of the structure and dynamic behavior of Petri net models. Coloring of Petri nets of all classes is powerful for multiscale modeling and for the representation of location and space in reaction networks since it combines the concept of Petri nets with the computational mightiness of a programming language. In the context of the Petri net framework, we provide two most recently developed approaches to biomodel engineering, the database-assisted automatic composition and modification of Petri nets with the help of reusable, metadata-containing modules, and the automatic reconstruction of networks based on time series data sets. With all these features the framework provides multiple options for biomodel engineering in the context of systems and synthetic biology.

Thermosolutal and binary fluid convection as a 2×2 matrix problem