A Note on Colored Petri Nets

In this paper we give an overview of some formal models of concurrent systems, that are derived from the classical Petri net model. Since several of these models are introduced by Petri and his group within General Net Theory [4] they can also be called 'high-level Petri nets'. We discuss the motivation and usefulness of such extensions, as well as some of their disadvantages. While many of these models are only informally presented, we give a more formal definition of self-modifying nets together with a new presentation. On the other hand we do not consider such models that are combinations of Petri nets with other models, such as the program schemata of Roucairol f213 or evaluation nets of Noe [19~ .

https://link.springer.com/content/pdf/10.1007%2F3-540-10856-4_80.pdf

Generalizations of Petri Nets

Process discovery techniques have successfully been applied in a range of domains to automatically discover process models from event data. Unfortunately existing discovery techniques only discover a behavioral perspective of processes, where the data perspective is often as a second-class citizen. Besides, these discovery techniques fail to deal with object-centric data with many-to-many relationships. Therefore, in this paper, we aim to discover a novel modeling language which combines data models with declarative models, and the resulting object-centric behavioral constraint model is able to describe processes involving interacting instances and complex data dependencies. Moreover we propose an algorithm to discover such models.

Automatic discovery of object-centric behavioral constraint models

Nowadays, information systems are widely used in various organizations to support the execution of their business processes. Therefore, the amount of data being stored about process executions is rapidly growing. Today’s main innovations are intelligently exploiting the data and turning data into real value. Process mining appears to leverage execution data to analyze the business processes executed on information systems. Existing process mining techniques make a fundamental assumption about processes. Process models and event logs assume the presence of a well-defined case notion. This implies that each event refers to a case and that the model describes the life-cycle of cases. This assumption is consistent with case-centric information systems, e.g., Workflow Management (WFM) systems. However, most information systems one encounters in enterprises nowadays are artifact-centric (or data-centric), e.g., Enterprise Resource Planning (ERP) systems, which do not assume a case notion in their business processes. Such differences lead to problems when applying existing process mining techniques, e.g., it is difficult to identify the case notion for the whole process, and the many-to-many relations cannot be well described. In order to solve these problems, we propose a series of process mining techniques in this thesis, such as a novel log format named eXtensible Object-Centric (XOC) to organize the data generated by artifact-centric information systems and a novel modeling language which combines data/object modeling languages (ER, UML, or ORM) and declarative languages (Declare). Besides, we propose approaches to automatically discover OCBC models from XOC logs, to check conformance and to analyze the performance. In summary, this thesis proposes new process mining techniques to analyze the data from artifact-centric information systems

Process mining based on object-centric behavioral constraint (OCBC) models

We survey formal frameworks for workflow modelling. We summarise important aspects of workflow management and approaches to evaluate current workflow management systems. We discuss a number of formalisms for workflow modelling, namely Petri nets, Temporal Logic, and Transaction Logic. We decribe how these formalisms are used specifically for workflow modelling, their possibilities and their disadvantages.

/pdf/formal-frameworks-for-workflow-modelling-1g2bmdnav7.pdf

Formal frameworks for workflow modelling

: The problem of representing reentrancy, recursivity and pipe-lining of control in asynchronous structures is examined with the intention of eliminating some of the drawbacks of the other solutions to their problems known so far. A model of concurrent systems having the capability of handling colored representations of control flow has been defined as an extension of an already existing model of parallel systems, the Petri Net Model. The structure and execution rules of Petri Nets have been modified in order to handle the colored tokens. (Author)

Keki B Irani

Papers

Colored Petri Nets: Their Properties and Applications.