3,857 research outputs found
On the Semantics of Petri Nets
Petri Place/Transition (PT) nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the "token game"' is too intensional, even in its more abstract interpretations in term of nonsequential processes and monoidal categories; on the other hand, Winskel's basic unfolding construction, which provides a coreflection between nets and finitary prime algebraic domains, works only for safe nets. In this paper we extend Winskel's result to PT nets. We start with a rather general category {PTNets} of PT nets, we introduce a category {DecOcc} of decorated (nondeterministic) occurrence nets and we define adjunctions between {PTNets} and {DecOcc} and between {DecOcc} and {Occ}, the category of occurrence nets. The role of {DecOcc} is to provide natural unfoldings for PT nets, i.e. acyclic safe nets where a notion of family is used for relating multiple instances of the same place. The unfolding functor from {PTNets} to {Occ} reduces to Winskel's when restricted to safe nets, while the standard coreflection between {Occ} and {Dom}, the category of finitary prime algebraic domains, when composed with the unfolding functor above, determines a chain of adjunctions between {PTNets} and {Dom}
Extension of Petri Nets by Aspects to Apply the Model Driven Architecture Approach
Within MDA models are usually created in the UML. However, one may prefer to\ud
use different notations such as Petri-nets, for example, for modelling concurrency\ud
and synchronization properties of systems. This paper claims that techniques that\ud
are adopted within the context of MDA can also be beneficial in modelling systems\ud
by using notations other than the UML. Petri-Nets are widely used for modelling\ud
of business and application logic of information systems with web services. For\ud
certain kinds of applications, therefore, Petri Nets can be more suitable for building\ud
Computation Independent, Platform Independent and Platform Specific Models\ud
(CIM, PIM and PSM). Unfortunately, the well-known problems with separation of\ud
concerns in Petri Nets and keeping track of changes may hinder achieving the aim of\ud
MDA: building reusable, portable and interoperable models. In this paper we define\ud
Aspect Petri Nets as a structure of several Petri Nets and quantification rules for\ud
weaving of those Petri Nets. Aspect Petri Nets are suitable for application of MDA;\ud
they support traceability of changes and reusability, portability and interoperability\ud
of models. We illustrate advantages of modelling in Aspect Petri Nets for MDA\ud
application and describe necessary tool support
Enhancing workflow-nets with data for trace completion
The growing adoption of IT-systems for modeling and executing (business)
processes or services has thrust the scientific investigation towards
techniques and tools which support more complex forms of process analysis. Many
of them, such as conformance checking, process alignment, mining and
enhancement, rely on complete observation of past (tracked and logged)
executions. In many real cases, however, the lack of human or IT-support on all
the steps of process execution, as well as information hiding and abstraction
of model and data, result in incomplete log information of both data and
activities. This paper tackles the issue of automatically repairing traces with
missing information by notably considering not only activities but also data
manipulated by them. Our technique recasts such a problem in a reachability
problem and provides an encoding in an action language which allows to
virtually use any state-of-the-art planning to return solutions
ACP Semantics for Petri Nets
The paper deals with algebraic semantics for Petri nets, based on process algebra ACP. The semantics is defined by assigning a special variable to every place of given Petri net, expressing the process initiated in the place. Algebraic semantics of the Petri net is then defined as a parallel composition of all the variables, where corresponding places hold tokens within the initial marking. Resulting algebraic specification preserves operational behavior of the original net-based specification
Finite petri nets as models for recursive causal behaviour
Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud
\ud
B=(a.nilb.B)+c.nil. \ud
\ud
We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence
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The use of Petri nets for modeling pipelined processors
This paper discusses the use of Petri Nets for modeling and analyzing pipelined processors. Petri Nets are particularly well-suited to modeling the synchronization, buffering, resource contention and delicate timing so common in pipelined processors. Tools for simulating, animating and analyzing the behavior of the models are described. The usefulness of the tools and the analysis methods they support in evaluating the performance and analyzing the detailed timing of pipelined microprocessors is illustrated through an example
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
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