Kurt Lautenbach

Elements of General Net Theory

Some of the main features of a theory of systems in which the concept of concurrency plays a central role are presented. This theory is founded upon a systems model called condition/event-systems (CE-systems).

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.

Liveness in Bounded Petri Nets Which Are Covered by T-Invariants

In this paper a criterion is introduced that is sufficient for the liveness in Petri nets which are bounded and covered by non-negative T-invariants.

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.

Reproducibility of the Empty Marking

The main theorem of the paper states that the empty marking O is reproducible in a p/t-net N if and only if there are reproducing T-invariants whose net representations have neither traps nor co-traps (deadlocks, siphons). This result is to be seen in connection to modeling processes, since all processes which have a start and a goal event usually reproduce the empty marking.

Logical reasoning and Petri nets

The main result of the paper states that a set F of propositional-logic formulas is contradictory iff in all net representations of F the empty marking is reproducible.

A Petri net representation of Bayesian message flows: importance of Bayesian networks for biological applications

This article combines Bayes’ theorem with flows of probabilities, flows of evidences (likelihoods), and fundamental concepts for learning Bayesian networks as biological models from data. There is a huge amount of biological applications of Bayesian networks. For example in the fields of protein modeling, pathway modeling, gene expression analysis, DNA sequence analysis, protein–protein interaction, or protein–DNA interaction. Usually, the Bayesian networks have to be learned (statistically constructed) from array data. Then they are considered as an executable and analyzable model of the data source. To improve that, this work introduces a Petri net representation for the propagation of probabilities and likelihoods in Bayesian networks. The reason for doing so is to exploit the structural and dynamic properties of Petri nets for increasing the transparency of propagation processes. Consequently the novel Petri nets are called “probability propagation nets”. By means of examples it is shown that the understanding of the Bayesian propagation algorithm is improved. This is of particular importance for an exact visualization of biological systems by Bayesian networks.

Timestamp nets in technical applications

Timestamp Petri nets, introduced in this paper, offer a new method to deal with time critical problems in the field of automation of manufacturing systems. To each token in a timestamp net a timestamp is assigned, which denotes the time when the token was put on its place. In those nets intervals are assigned to the incoming edges of transitions, which describe the permeability of the edge relative to the token on the adjacent place. In timestamp nets it is possible that synchronizing transitions are not able to fire although they are supplied with tokens sufficiently, because their incoming edges are not permeable simultaneously. In this case we say the transition got timewise stuck. In this paper it is examined how transitions of a timestamp net are getting timewise stuck. Based on a symbolic analysis, these investigations can be reduced to solving systems of linear inequalities. The method can also be used to determine parameters for a timestamp net in order to prevent transitions from getting timewise stuck. We show the methods applicability by the dynamic model of a small technical plant as an example. Forbidden states of the uncontrolled system are described by transitions which can get timewise stuck. We use the method to determine time parameters of a controller, which ensures that forbidden states in the controlled system are unreachable.

Using Parameterized Timestamp Petri Nets in Automatic Control

In the following sections, we describe a method to deal with time critical problems in the field of automatic control of manufacturing systems. The behavior of a technical system is represented by Timestamp Petri Nets. With the aid of a symbolic analysis of such nets we generate a linear optimization problem from a system of inequalities. Their solutions imply time parameters for software controllers which avoid the occurrence of dangerous situations. We show the applicability of the method with a small example where unknown time parameters of a controller have to be determined in order to avoid forbidden states of the controlled system.