Jörg Desel

Lectures on Concurrency and Petri Nets

Over the last decade there has been a shift from “data-aware” information systems to “process-aware” information systems. To support business processes an enterprise information system needs to be aware of these processes and their organizational context. Business Process Management (BPM) includes methods, techniques, and tools to support the design, enactment, management, and analysis of such operational business processes. BPM can be considered as an extension of classical Workflow Management (WFM) systems and approaches. This tutorial introduces models, systems, and standards for the design, analysis, and enactment of workflow processes. Petri nets are used for the modeling and analysis of workflows. Using Petri nets as a formal basis, contemporary systems, languages, and standards for BPM and WFM are discussed. Although it is clear that Petri nets can serve as a solid foundation for BPM/WFM technology, in reality systems, languages, and standards are developed in an ad-hoc fashion. To illustrate this XPDL, the “Lingua Franca” proposed by the Workflow Management Coalition (WfMC), is analyzed using a set of 20 basic workflow patterns. This analysis exposes some of the typical semantic problems restricting the application of BPM/WFM technology.

Place or Transition Petri Nets

This contributions provides an introduction to the theory of place/transition Petri nets. Topics include the sequential and the concurrent behavior of place/ transition Petri nets, marking graphs and coverability trees, and some analysis techniques that are based on the structure of place/transition Petri nets.

Process mining based on regions of languages

In this paper we give an overview, how to apply region based methodsfor the synthesis of Petri nets from languages to process mining. The research domain of process mining aims at constructing a process modelfrom an event log, such that the process model can reproduce the log, and doesnot allow for much more behaviour than shown in the log. We here considerPetri nets to represent process models. Event logs can be interpreted as finite languages.Region based synthesis methods can be used to construct a Petri net froma language generating the minimal net behaviour including the given language.Therefore, it seems natural to apply such methods in the process mining domain.There are several different region based methods in literature yielding differentPetri nets. We adapt these methods to the process mining domain and comparethem concerning efficiency and usefulness of the resulting Petri net.

The synthesis problem of Petri nets

The synthesis problem of concurrent systems is the problem of synthesizing a concurrent system model from sequential observations. The paper studies the synthesis problem for elementary Petri nets and transition systems. A characterization of the class of transition systems which correspond to elementary Petri nets is proven. It is shown how to generate all elementary Petri nets corresponding to a given transition system. If there is any such elementary Petri net, it is proven that there always exists a small one which has only polynomially many elements in the size of the transition system.

What Is a Petri Net? Informal Answers for the Informed Reader

The increasing number of Petri net variants naturally leads to the question whether the term “Petri net” is more than a common name for very different concepts. This contribution tries to identify aspects common to all or at least to most Petri nets. It concentrates on those features where Petri nets significantly differ from other modeling languages, i.e. we ask where the use of Petri nets leads to advantages compared to other languages. Different techniques that are usually comprised under the header “analysis” are distinguished with respect to the analysis aim. Finally, the role of Petri nets in the development of distributed systems is discussed.

Modeling, Simulation and Analysis of Business Processes

Building and analyzing models of business processes has gained increased importance for any activity that requires a close examination of the business processes involved, e.g., Business Process Reengineering efforts. In this chapter we introduce a Petri net based approach to support such activities. Business processes are modeled using standard place/transition nets enhanced with some notions needed to integrate all aspects of business processes that are relevant with respect to analysis purposes, e.g., the notion of time and costs. The Petri net models of business processes are simulated by generating partially ordered runs. We will show how these runs can then be used for performance analysis of important key indicators such as throughput time. All introduced concepts are summarized in a 3-step approach that supports users to base their decision between possible alternatives for the design of a business process on facts.

Partial order behaviour and structure of Petri nets

This paper argues that partial order semantics can be used profitably in the proofs of some nontrivial results in Petri net theory. We show that most of Commoners and Hacks structure theory of free choice nets can be phrased and proved in terms of partial order behaviour. The new proofs are considerably shorter (and, arguably, more lucid) than the old ones; they also generalise the results from (safe) free choice nets to (bounded) extended free choice nets.

A Proof of the Rank Theorem for Extended Free Choice Nets

A net is called well-formed if it can be marked with a live and bounded marking. The Rank Theorem characterises well-formed extended free choice nets, employing only the linear algebraic representation of a net. The paper presents a proof of the Rank Theorem which is based on the characterisation of liveness by deadlocks and traps and the coverability of well-formed extended free choice nets by S- and T-components. Consequences of the Rank Theorem include the Duality Theorem, a polynomial algorithm for deciding wellformedness, and simple proofs of other results concerning extended free choice nets. Moreover, the Rank Theorem implies a sufficient condition for liveness which applies to arbitrary nets.

Validation of Process Models by Construction of Process Nets

The major aim of this chapter is to describe an approach towards the development of techniques and tools to support the construction, validation and the verification of Petri net models of information systems and business processes. To this end, the behavior of the models is defined by partially ordered causal runs, represented by process nets. We discuss how these runs are constructed and visualized for validation purposes, and how they are analyzed. Moreover, we demonstrate how different dynamic properties can be formulated and checked by searching respective patterns in process nets.

Reachability in cyclic extended free-choice systems

The reachability problem for Petri nets can be stated as follows: Given a Petri net (N, M 0 ) and a marking M of N, does M belong to the state space of (N, M 0 )? We give a structural characterisation of reachable states for a subclass of extended free-choice Petri nets. The nets of this subclass are those enjoying three properties of good behaviour: liveness, boundedness and cyclicity. We show that the reachability relation can be computed from the information provided by the S-invariants and the traps of the net. This leads to a polynomial algorithm to decide if a marking is reachable