Modeling production configuration using nested colored object-oriented Petri-nets with changeable structures

Configuring production processes based on process platforms has been well recognized as an effective means for companies to provide product variety while maintaining mass production efficiency. The production processes of product families involve diverse variations in manufacturing and assembly processes resulted from a large variety of component parts and assemblies. This paper develops a multilevel system of nested colored object-oriented Petri nets with changeable structures to model the configuration of production processes. To capture the semantics associated with production configuration decisions, some unique modeling mechanisms are employed, including colored Petri nets, object-oriented Petri nets, changeable Petri net structures, and net nesting. The modeling formalism comprises resource nets, manufacturing nets, assembly nets and process nets. The paper demonstrates how these net definitions are applied to the specification of production process variants at different levels of abstraction. Also reported is a case study in an electronics company. The system model is further analyzed with focus on conflict prevention and deadlock detection.     

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.     

Petri nets, algebras, morphisms, and compositionality

It is shown how a category of Petri nets can be viewed as a subcategory of two sorted algebras over multisets. This casts Petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition—the morphisms here respect the behaviour of nets. The categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components; for example, various forms of parallel composition of Petri nets arise naturally from the product in the category. This abstract setting makes plain a useful functor from the category of Petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of Petri nets—for instance, the coloured and higher level nets of Kurt Jensen arise through a simple modification of the sorts of the algebras underlying nets. Further, it provides a smooth formal relation with other models of concurrency such as Milner's calculus of communicating systems (CCS) and Hoare's communicating sequential processes (CSP), though this is only indicated in this paper.     

基于知识Petri网和归结规则的推理方法

本文提出了一种基于知识Petri网和归结规则的推理方法.通过知识Petri网描述命题逻辑知识库,将归结规则映射到知识Petri网上,根据库所和变迁的连接关系,定义了知识Petri网中的归结结构.利用归结结构,给出了基于知识Petri网的归结推理算法和扩展知识库的推理算法,并利用Wumpus实例验证了推理算法.该推理方法是可靠且完备的,能够利用知识Petri网的网络结构降低计算复杂性.     

Petri nets,event structures and domains,part I

The general aim of this paper is to find a theory of concurrency combining the approaches of Petri and Scott (and others).In part I we introduce our formalisms. To connect the abstract ideas of events and domains of information, we show how casual nets induce certain kinds of domains where the information points are certain sets of events. This allows translations between the languages of net theory and domain theory. Following the idea that events of causal nets are occurrences, we generalise causal nets to occurrence nets, by adding forwards conflict. Just as infinite flow charts unfold finite ones, so transition nets can be unfolded into occurrence nets. Next we extend the above connections between nets and domains to these new nets. Event structures which are intermediate between nets and domains play an important part in all our work. Finally, as an example of how concepts translate from one formalism to the other, we show how Petri's notion of confusion ties up with Kahn and Plotkin's concrete domains.In part II we shall continue the job of connecting up notions within net theory and the theory of domains. In particular, we shall examine the idea of states of computations.     

True-concurrency probabilistic models: Markov nets and a law of large numbers

We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the true-concurrency semantics—this means that traces, not firing sequences, are given a probability. This model builds upon our previous work on probabilistic event structures. We use the notion of a branching cell for event structures, and show that the latter provides an adequate conception of local state for nets. We prove a Law of Large Numbers (LLN) for Markov nets, which constitutes the main contribution of the paper. This LLN allows for the characterization, in a quantitative way, of the asymptotic behavior of Markov nets.     

Step semantics of boolean nets

Boolean nets are a family of Petri net models with very simple markings which are sets of places. We investigate several classes of boolean nets distinguished by different kinds of individual connections between places and transitions, as well as different ways in which these connections are combined in order to specify the effect of executing steps of transitions. The latter aspect can be captured by connection monoids. A key advantage of using connection monoids is that by describing the step semantics of a class of Petri nets in terms of a connection monoid, one can apply results developed within a general theory of Petri net synthesis. In this paper, we provide an extensive classification of boolean nets which can be described by connection monoids. This classification is based on the realisation that the different ways of interpreting combinations of connections can be made explicit using a higher level monoid. Moreover, we demonstrate that connection monoids can capture other behavioural properties of boolean nets, such as structural conflicts between transitions.     

Verification of computing grids with special edge conditions by infinite Petri nets

A technique of the computing grids verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structurally conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented using p-invariants of modified nets.     

A Survey of Petri Net Methods for Controlled Discrete Event Systems

This paper surveys recent research on the application of Petri net models to the analysis and synthesis of controllers for discrete event systems. Petri nets have been used extensively in applications such as automated manufacturing, and there exists a large body of tools for qualitative and quantitative analysis of Petri nets. The goal of Petri net research in discrete event systems is to exploit the structural properties of Petri net models in computationally efficient algorithms for computing controls. We present an overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets. We describe two basic approaches for controller synthesis, based on state feedback and event feedback. We also discuss two efficient techniques for the on-line computation of the control law, namely the linear integer programming approach which takes advantage of the linear structure of the Petri net state transition equation, and path-based algorithms which take advantage of the graphical structure of Petri net models. Extensions to timed models are briefly described. The paper concludes with a discussion of directions for future research.     

Compositional Petri Net Approach to the Development of Concurrent and Distributed Systems

In the paper, a formal model based on Petri nets is proposed in the context of a compositional approach to the development and analysis of complex concurrent and distributed systems. Mutlilabels of Petri nets are introduced allowing labeling a transition not only with a single symbol, but also with a multiset of symbols. Operations on multilabeled Petri nets—parallel composition and restriction—are defined. A definition of a Petri net entity is given based on the notion of multilabels. A Petri net entity is a Petri net with a set of multilabels, where each multilabel is regarded as an access point of the entity. The operation of entity composition is introduced. Equivalence of entities is defined based on bisimulation equivalence of Petri nets. It is shown that the equivalence relation is congruent with respect to entity composition. It is also demonstrated that the composition operation is commutative and associative.     

An algebraic approach to revising propositional rule-based knowledge bases

One of the important topics in knowledge base revision is to introduce an efficient implementation algorithm. Algebraic approaches have good characteristics and implementation method; they may be a choice to solve the problem. An algebraic approach is presented to revise propositional rule-based knowledge bases in this paper. A way is firstly introduced to transform a propositional rule-based knowledge base into a Petri net. A knowledge base is represented by a Petri net, and facts are represented by the initial marking. Thus, the consistency check of a knowledge base is equivalent to the reachability problem of Petri nets. The reachability of Petri nets can be decided by whether the state equation has a solution; hence the consistency check can also be implemented by algebraic approach. Furthermore, algorithms are introduced to revise a propositional rule-based knowledge base, as well as extended logic programming. Compared with related works, the algorithms presented in the paper are efficient, and the time complexities of these algorithms are polynomial.     

Net models of discrete information transducers. I

Dynamic net models of a special kind — discrete process generators — are considered. Their relation to automata, Petri nets, partially commutative monoids, and the theory of traces is examined.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 83–90, September–October, 1991.     

On the ω-language Expressive Power of Extended Petri Nets

In this paper, we study the expressive power of several monotonic extensions of Petri nets. We compare the expressive power of Petri nets, Petri nets extended with non-blocking arcs and Petri nets extended with transfer arcs, in terms of ω-languages. We show that the hierarchy of expressive powers of those models is strict. To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.     

Petri net representation of multi-valued logical regulatory graphs

Relying on a convenient logical representation of regulatory networks, we propose a generic method to qualitatively model regulatory interactions in the standard elementary and coloured Petri net frameworks. Logical functions governing the behaviours of the components of logical regulatory graphs are efficiently represented by Multivalued Decision Diagrams, which are also at the basis of the translation of logical models in terms of Petri nets. We further delineate a simple strategy to sort trajectories through the introduction of priority classes (in the logical framework) or priority functions (in the Petri net framework). We also focus on qualitative behaviours such as multistationarity or sustained oscillations, identified as specific structures in state transition graphs (for logical models) or in marking graphs (in Petri nets). Regulatory circuits are known to be at the origin of such properties. In this respect, we present a method that allows to determine the functionality contexts of regulatory circuits, i.e. constraints on external regulator states enabling the corresponding dynamical properties. Finally, this approach is illustrated through an application to the modelling of a regulatory network controlling T lymphocyte activation and differentiation.     

Well-structured languages

This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.     

On the Regularity of Petri Net Languages

Petri nets are known to be useful for modeling concurrent systems. Once modeled by a Petri net, the behavior of a concurrent system can be characterized by the set of all executable transition sequences, which in turn can be viewed as a language over an alphabet of symbols corresponding to the transitions of the underlying Petri net. In this paper, we study the language issue of Petri nets from a computational complexity viewpoint. We analyze the complexity of theregularity problem(i.e., the problem of determining whether a given Petri net defines an irregular language or not) for a variety of classes of Petri nets, includingconflict-free,trap-circuit,normal,sinkless,extended trap-circuit,BPP, andgeneralPetri nets. (Extended trap-circuit Petri nets are trap-circuit Petri nets augmented with a specific type ofcircuits.) As it turns out, the complexities for these Petri net classes range from NL (nondeterministic logspace), PTIME (polynomial time), and NP (nondeterministic polynomial time), to EXPSPACE (exponential space). In the process of deriving the complexity results, we develop adecomposition approachwhich, we feel, is interesting in its own right, and might have other applications to the analysis of Petri nets as well. As a by-product, an NP upper bound of the reachability problem for the class of extended trap-circuit Petri nets (which properly contains that of trap-circuit (and hence, conflict-free) and BPP-nets, and is incomparable with that of normal and sinkless Petri nets) is derived.     

Deciding a class of path formulas for conflict-free petri nets

The aim of this paper is to develop a unified approach for deriving complexity results for problems concerning conflict-free Petri nets. To do so, we first define a class of formulas for paths in Petri nets. We then show that answering the satisfiability problem for conflict-free Petri nets is tantamount to solving a system of linear inequalities (which is known to be in P). Since a wide spectrum of Petri net problems (including various fairness-related problems) can be reduced to the satisfiability problem in a straightforward manner, our approach offers an umbrella under which many Petri net problems for conflict-free Petri nets can be shown to be solvable in polynomial time. As a side-product, our analysis provides evidence as to why detecting unboundedness for conflict-free Petri nets is easier (provided P ≠ NP) than for normal and sinkless Petri nets (which are two classes that properly contain conflict-free Petri nets). A preliminary version was presented at the 14th International Conference on Application and Theory of Petri Nets, Chicago, IL, USA, June 1993.