In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

Term Rewriting Systems

Petri nets for modeling of dynamic systems—a survey

技術解説 IEEE Computer

In this paper we discuss the issue of interleaving semantics versus True concurrency in an algebraic setting. We present various equivalence notions on Petri nets which can be used in the construction of algebraic models:

(a)

the occurrence net equivalence of Nielsen, Plotkin & Winskel;




(b)

bisimulation equivalence, which leads to a model which is isomorphic to the graph model of Baeten, Bergstra & Klop;




(c)

the concurrent bisimulation equivalence, which is also described by Nielsen & Thiagarajan, and Goltz;




(d)

partial order equivalences which are inspired by work of Pratt, and Boudol & Castellani.

Petri net models for algebraic theories of concurrency

Performance and cost analysis are the two main purposes of business process modeling, where the Petri net extended with time information is an effective tool for performance analysis, but not for cost analysis. This paper proposes a time Petri net extended with price information—Price Time Petri Net. Firstly, this paper associates a price with a time transition, and gives the semantics for price time Petri net in terms of priced timed transition systems. Then it defines a priced state class as an extension of state class, and discusses the soundness and completeness for this extension. An algorithm is given to prove that the minimum-cost reachability problem for bounded price time Petri net is decidable. Finally, this paper gives an example and draws a conclusion that incorporating price information in time Petri net and applying price time Petri net to business process management

/pdf/a-time-petri-net-extended-with-price-information-3os5kmtrky.pdf

A Time Petri Net Extended with Price Information

From the Publisher: 
Formal methods for the specification and verification of hardware and software systems are becoming more and more important as systems increase in size and complexity. The aim of the book is to illustrate progress in formal methods, based on Petri net formalisms. It contains a collection of examples arising from different fields, such as flexible manufacturing, telecommunication and workflow management systems. The book covers the main phases in the life cycle of design and implementation of a system, i.e., specification, model checking techniques for verification, analysis of properties, code generation, and execution of models. These techniques and their tool support are discussed in detail including practical issues. Amongst others, fundamental concepts such as composition, abstraction, and reusability of models, model verification, and verification of properties are systematically introduced.

Petri nets for Systems Engineering : A Guide to Modeling, Verification, and Applications (China Version)

From the Publisher:
Formal methods for the specification and verification of hardware and software systems are becoming more and more important as systems increase in size and complexity. The aim of the book is to illustrate progress in formal methods, based on Petri net formalisms. It contains a collection of examples arising from different fields, such as flexible manufacturing, telecommunication and workflow management systems. The book covers the main phases in the life cycle of design and implementation of a system, i.e., specification, model checking techniques for verification, analysis of properties, code generation, and execution of models. These techniques and their tool support are discussed in detail including practical issues. Amongst others, fundamental concepts such as composition, abstraction, and reusability of models, model verification, and verification of properties are systematically introduced.

Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications

ion, however, has a meaningful interpretation. To give an example, consider the fragment of a net in Figure 2.13a. Intuitively the abstraction in 2.4 Refinement and Composition 21 Figure 2.13d has a corresponding behaviour ("a token is passed through"). Figure 2.13d is also an abstraction of Figure 2.13b, but now the behaviour is different. In Figure 2.13d a token can pass, but not so in Figure 2.13b. Note that the set Y to be abstracted is not necessarily connected as a subgraph. However, Figure 2.13d can be interpreted as a merge of two places. This operation is called a fusion of places or place fusion. It will be used in Part II of this book to create larger nets from smaller ones. This kind of abstraction will be represented graphically as shown in Figure 2.13c. The dual situation for a transition-bordered set is shown in Figures 2.13e-h. Thus Figures 2.13f, g and h describe a fusion of transitions or transition fusion. -1 -I

Petri nets for systems engineering

In this paper, we show how to model with a timed Petri net, tasks, resources and constraints of a scheduling problem.

Modelling scheduling problems with timed Petri nets

This paper deals with the compositionality of liveness when synchronizing two colored FIFO nets. The composition operator allows to merge transitions as well as some adjacent places or queues.

Claude Girault

Papers

Petri nets for Systems Engineering : A Guide to Modeling, Verification, and Applications (China Version)

Petri Nets for Systems Engineering: A Guide to Modeling, Verification, and Applications

Petri nets for systems engineering

Modelling scheduling problems with timed Petri nets

Behavioural and Structural Composition Rules Preserving Liveness by Synchronization for Colored FIFO Nets