3 research outputs found
Morphisms of Coloured Petri Nets
We introduce the concept of a morphism between coloured nets. Our definition
generalizes Petris definition for ordinary nets. A morphism of coloured nets
maps the topological space of the underlying undirected net as well as the
kernel and cokernel of the incidence map. The kernel are flows along the
transition-bordered fibres of the morphism, the cokernel are classes of
markings of the place-bordered fibres. The attachment of bindings, colours,
flows and marking classes to a subnet is formalized by using concepts from
sheaf theory. A coloured net is a sheaf-cosheaf pair over a Petri space and a
morphism between coloured nets is a morphism between such pairs. Coloured nets
and their morphisms form a category. We prove the existence of a product in the
subcategory of sort-respecting morphisms. After introducing markings our
concepts generalize to coloured Petri nets
Model Checking of Boolean Process Models
In the field of Business Process Management formal models for the control
flow of business processes have been designed since more than 15 years. Which
methods are best suited to verify the bulk of these models? The first step is
to select a formal language which fixes the semantics of the models. We adopt
the language of Boolean systems as reference language for Boolean process
models. Boolean systems form a simple subclass of coloured Petri nets. Their
characteristics are low tokens to model explicitly states with a subsequent
skipping of activations and arbitrary logical rules of type AND, XOR, OR etc.
to model the split and join of the control flow. We apply model checking as a
verification method for the safeness and liveness of Boolean systems. Model
checking of Boolean systems uses the elementary theory of propositional logic,
no modal operators are needed. Our verification builds on a finite complete
prefix of a certain T-system attached to the Boolean system. It splits the
processes of the Boolean system into a finite set of base processes of bounded
length. Their behaviour translates to formulas from propositional logic. Our
verification task consists in checking the satisfiability of these formulas. In
addition we have implemented our model checking algorithm as a java program.
The time needed to verify a given Boolean system depends critically on the
number of initial tokens. Because the algorithm has to solve certain
SAT-problems, polynomial complexity cannot be expected. The paper closes with
the model checking of some Boolean process models which have been designed as
Event-driven Process Chains
Free Choice Petri Nets without frozen tokens and Bipolar Synchronization Systems
Bipolar synchronization systems (BP-systems) constitute a class of coloured
Petri nets, well suited for modeling the control flow of discrete, dynamical
systems. Every BP-system has an underlying ordinary Petri net, which is a
T-system. Moreover, it has a second ordinary net attached, which is a
free-choice system. We prove that a BP-system is live and safe if the T-system
and the free-choice system are live and safe and if the free-choice system has
no frozen tokens. This result is the converse of a theorem of Genrich and
Thiagarajan and proves an elder conjecture. The proof compares the different
Petri nets by Petri net morphisms and makes use of the classical theory of
free-choice system