Hartmann J. Genrich

System modelling with high-level Petri nets

Abstract The paper presents a high-level Petri net model of concurrent systems called predicate /transition-nets (PrT-nets). Its places represent variable properties of, or relations between, individuals; they are ‘predicates’ with variable extension. The transitions represent classes of elementary changes of those extensions. The model is introduced on the basis of a simple example from resource management. The central part of the paper is devoted to linear-algebraic techniques for verifying invariant assertions, yielding a calculus of S-invariants for PrT-nets. Finally, these modelling and analysis techniques are applied to a scheme for organizing a distributed data base taken from literature.

Predicate/Transition Nets

The paper deals with conceptual, mathematical and practical aspects of developing a net theoretic system model. The model presented is based on common techniques of modelling static systems as structured sets of individuals (relational structures). These structures are ‘dynamised’ by allowing some relations between individuals to be changed by the processes of the modelled system.

The Analysis of Distributed Systems by Means of Predicate ? Transition-Nets

Within the framework of net-semantics of models of dynamic systems, the present paper introduces a new standard interpretation of nets called predicate/transition-nets (Pr/T-nets). These nets are schemes of ‘ordinary’ Petri nets. The places (circles) of Pr/T-nets represent changing properties of, or relations between, individuals; they are ‘predicates’ with variable extension. A current case of a system modelled by a Pr/T-net is denoted by marking the places with those tuples of individual symbols for which the respective predicates hold in that case. The transitions (boxes) are schemes of elementary changes of markings constituting the processes carried by the system. Instances of these schemes are generated by means of consistent substitution of individual variables by symbols.

Executable Petri net models for the analysis of metabolic pathways

Abstract.Computer-assisted simulation of biochemical processes is a means to augment the knowledge about the control mechanisms of such processes in particular organisms. This knowledge can be helpful for the goal-oriented design of drugs. Normally, continuous models (differential equations) are chosen for modelling such processes. The application of discrete event systems such as Petri nets has been restricted in the past to low-level modelling and qualitative analysis. To demonstrate that Petri nets are indeed suitable for simulating metabolic pathways, the glycolysis and citric acid cycle are selected as well-understood examples of enzymatic reaction chains (metabolic pathways). The paper discusses the steps that lead from gaining necessary knowledge about the involved enzymes and substances, to establishing and tuning high-level net models, to performing a series of simulations, and finally to analysing the results. We show that the consistent application of the Petri net view to these tasks has certain advantages, and – using advanced net tools – reasonable simulation times can be achieved.

Concurrency and Nets

Many approaches are being developed for handling the different phases in the design of complex information systems, namely specification, verification, evaluation, implementation and testing. These approaches are more or less applicable to the various specific aspects of the design phases and partially supported by efficient tools. This paper deals with one of the most important approaches used in the design of information systems, i. e., the Petri net based models approach, which proves particularly interesting. It is indicated how Petri net based models are used to represent systems behavior and then some of the resulting advantages are given. Furthermore, it is emphasized why and how a Petri net based approach can support all the design phases and it is made clear for which purposes and in which applications Petri net based designs are important. are also given. A few illustrative examples

A theory of bipolar synchronization schemes

The aim is to better understand the relationships between choice and concurrency that lead to the good behaviour of distributed systems. In order to do so, we formulate a model based on Petri nets and develop its theory. The model is called bipolar synchronization schemes (bp schemes) and the theory we construct is mainly devoted to synthesising, in a systematic fashion, all well behaved bp schemes. We also provide a computational interpretation of well behaved bp schemes. Through this interpretation the insights gained by developing the theory of bp schemes can be transferred to concurrent programs.

The calculus of facts

Nets of conditions and events (‘special’ Petri nets) are widely used models of dynamic systems. They represent the causal structure of the concurrent operation and co-operation of the components of a system. In this paper we introduce a net theoretic version of the first-order predicate calculus. Its purpose is to offer a formal language for expressing the relationship between a net model and the modelled system, and to provide rules for deriving the logical consequences of such an interpretation in a way that the results are expressed in the same language as the model, namely the net language. By this we permit the use of symbolic logic as part of a general formalism for the analysis and specification of dynamic systems. We show how ‘static’ logic can be correctly applied even in those practically important dynamic contexts where certain sentences change their truthvalues in a not fully specified order. As a useful by-product the graphical representation of nets induces a very natural graphical representation of the predicate calculus.

S-Invariance in Predicate/Transition Nets

In any theory of dynamic systems, the notion of invariance is of central importance. Given a class of processes, the supporting system is determined by what is invariable with respect to the processes.

Formal Verification of an Arbiter Cascade

The asynchronous access of a group of users (e.g. processors) to a single resource (e.g. bus) is regulated by a cascade of arbiters. A single arbiter circuit handles two users. The cascade permits any number of users to be serviced. We use a hierarchical Colored Petri Net to describe the arbiter circuit and the protocol for using it. We also describe the layout of a 2d input cascade of (2d-1) arbiters, d≥1 being the depth of the cascade. We verify the proper functioning of the cascade, first for depth d=1 using an occurrence graph analyzer to prove crucial invariants and confonmance to the protocol; then for arbitrary depth using mathematical induction. As an alternative proof, we develop equivalent Petri net substitutes for the building blocks of the design and verify the resultant special net using classical net theoretic methods. Based on the verification we propose a change of the arbiter to speed-up the cascade.

Verification of Recipe-Based Control Procedures by Means of Predicate/Transition Nets

The paper presents a method for the verification of control procedures which are based on so-called recipes. The concept of recipes is widely used in the control of multipurpose chemical batch plants which are very similar to Flexible Manufacturing Systems.