Kathrin Hoffmann

High-level nets with nets and rules as tokens

High-Level net models following the paradigm “nets as tokens” have been studied already in the literature with several interesting applications. In this paper we propose the new paradigm “nets and rules as tokens”, where in addition to nets as tokens also rules as tokens are considered. The rules can be used to change the net structure. This leads to the new concept of high-level net and rule systems, which allows to integrate the token game with rule-based transformations of P/T-systems. The new concept is based on algebraic high-level nets and on the main ideas of graph transformation systems. We introduce the new concept with the case study “House of Philosophers”, a dynamic extension of the well-known dining philosophers. In the main part we present a basic theory for rule-based transformations of P/T-systems and for high-level nets with nets and rules as tokens leading to the concept of high-level net and rule systems.

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.

Algebraic Higher-Order Nets: Graphs and Petri Nets as Tokens

Petri nets and Algebraic High-Level Nets are well-known to model parallel and concurrent systems. In this paper, we introduce the concept of Algebraic Higher-Order Nets, which allow to have dynamical tokens like graphs or (ordinary low-level) Petri nets. For this purpose, we specify graphs and Petri nets in the higher-order algebraic specification language HasCasl such that graphs and Petri nets become first-class citizens, i.e. members of algebras (rather than algebras themselves). As an example, we model hospital therapeutic processes by a single higher-order net. Individual care plans for each patient are tokens modeled by low-level nets.

Petri Net Transformations

Abstract Petri Nets: A Uniform Approach and Rule-Based Refinement. PhD thesis, Technical University Berlin, 1996. Shaker Verlag. [23] J. Padberg. Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems. Applied Categorical Structures, 7(4):371-403, 1999. [24] J. Padberg. Basic Ideas for Transformations of Specification Architectures. In Proc.Workshop on Software Evolution through Transformations (SET 02), volume 74 of ENTCS, 2002. [25] J. Padberg, H. Ehrig, and L. Ribeiro. Algebraic High-Level Net Transformation Systems. Mathematical Structures in Computer Science, 5(2):217-256, 1995. [26] J. Padberg, P. Schiller, and H. Ehrig. New Concepts for High-Level Petri Nets in the Application Domain of Train Control. In Proc. Symposium on Transportation Systems, pages 153-160, 2000. [27] J. Padberg and M. Urbasek. Rule-Based Refinement of Petri Nets: A Survey. In Proc. Petri Net Technology for Communication-Based Systems, volume 2472 of LNCS, pages 161-196. Springer, 2003. [28] W. Reisig. Petri Nets and Algebraic Specifications.

Transformations in Reconfigurable Place/Transition Systems

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements. For the transformation of Petri nets in the double pushout approach, the categorical framework of adhesive high-level replacement systems has been instantiated to Petri nets. In this paper, we show that also place/transition systems form a weak adhesive high-level replacement category. This allows us to apply the developed theory also to tranformations within reconfigurable place/transition systems.

Applying algebraic approaches for modeling workflows and their transformations in mobile networks

In emergency scenarios we can obtain a more effective coordination among team members, each of them equipped with hand-held devices, through the use of workflow management software. Team members constitute a Mobile Ad-hoc NETwork (MANET), whose topology both influences and is influenced by the workflow. In this paper we propose an algebraic approach for modeling workflow progress as well as its modifications as required by topology transformations. The approach is based on Algebraic Higher-Order Nets and sees both workflows and topologies as tokens, allowing their concurrent modification.

Stepwise Introduction and Preservation of Safety Properties in Algebraic High-Level Net Systems

Our approach of rule-based refinement provides a formal description for the stepwise system development based on Petri nets. Rules with a left-hand and a right-hand side allow replacing subnets in a given algebraic high-level net system. The extension of these rules supports the preservation of system properties. In this paper we extend the preservation of safety properties significantly. We define rules, that introduce new safety properties. In our new approach we propose first the verification of properties at the moment they can be expressed and then their preservation further on. Hence, properties can be checked as long as the system is still small. Moreover, introducing properties allows checking these for the relevant subpart only. Changes that are required later on can be treated the same way and hence preserve the system properties. Hence, we have made a step towards a formal technique for the stepwise system development during analysis and design.

Run Time Modification of Algebraic High Level Nets and Algebraic Higher Order Nets using Folding and Unfolding Construction

In this paper we extend the well defined formalism of Algebraic High Level Nets by higher order functions. The resulting formalism of Algebraic Higher Order Net leads to a more flexible modeling technique, which is new in the area of business processes. The main results of this paper are on the one hand the relationship between Algebraic High Level Nets and a restricted class of Algebraic Higher Order Nets given by folding and unfolding and on the other hand the concept of run time modification, which allows to modify existing models of flexible business processes in a formal way.

Higher-Order Nets for Mobile Policies

Since the early 80s the combination of Petri nets and rule-based transformations has been extensively researched to obtain new concepts and results. In this paper we consider rules as tokens leading to the concept of higher-order nets for mobile policies. The rules are used on the one hand for the specification of policy rules and on the other hand for the modification of policy rules, i.e. for the definition of new rules by reusing existing rules. So the higher-order net models distribution and modification of policy rules in a systematic and structured way. We give HasCasl-specifications of rules and (local) transformations in the sense of the double-pushout approach and illustrate our concept by a small system inspired by the case study of a tax refund process E. Bertino, E. Ferrari, E., and V. Atluri. The Specification and Enforcement of Authorization Constraints in Workflow Management Systems. ACM Transactions on Information and System Security 2 (1) (1999) 65--104].

Negative Application Conditions for Reconfigurable Place/Transition Systems

This paper introduces negative application conditions for reconfigurable place/transition nets. These are Petri nets together with a set of rules that allow changing the net and its marking dynamically. Negative application conditions are a control structure that prohibits the application of a rule if certain structures are already existent. We motivate the use of negative application conditions in a short example. Subsequently the underlying theory is sketched and the results – concerning parallelism, concurrency and confluence – are presented. Then we resume the example and explicitly discuss the main results and their usefulness within the example.