Related papers: Network Models from Petri Nets with Catalysts
Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…
The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the…
The formalism of the models with Petri networks provides a sound theoretical base, supported by powerful mathematical methods able to extract information necessary for the formalism and simulation of the real system that provides features…
We show how a particular variety of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category --…
This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent,…
Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned "rate constants", any…
Many categorical frameworks have been proposed to formalize the idea of gluing Petri nets with each other. Such frameworks model net gluings in terms of sharing of resources or synchronization of transitions. Interpretations given to these…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
We present a unified framework for Petri nets and various variants, such as pre-nets and Kock's whole-grain Petri nets. Our framework is based on a less well-studied notion that we call $\Sigma$-nets, which allow finer control over whether…
In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these operads is called a \emph{network model}, a monoidal variant of…
Concurrent programming is used in all large and complex computer systems. However, concurrency errors and system failures (ex: crashes and deadlocks) are common. We find that Petri nets can be used to model concurrent systems and find and…
In many complex systems that can be modeled using Petri nets time can be a very important factor which should be taken into account during creation and analysis of the model. Time data can describe starting moments of some actions or their…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
We describe a modular modelling approach permitting curation, updating, and distributed development of modules through joined community effort overcoming the problem of keeping a combinatorially exploding number of monolithic models up to…
A new formalism of Petri nets, based on the adoption of the "position-arc-transition" triad and "transition-arc-position" triad as structure-forming units is introduced. In accordance with the Fusion principle, an analytical representation…
Developing algorithms for distributed systems is an error-prone task. Formal models like Petri nets with transits and Petri games can prevent errors when developing such algorithms. Petri nets with transits allow us to follow the data flow…
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a…
It is well known that the complex system operation requires the use of new scientific tools and computer simulation. This paper presents a modular approach for modeling and analysis of the complex systems (in communication or transport…
It is well known that the complex system operation requires the use of new scientific tools and computer simulation. This paper presents a modular approach for modeling and analysis of the complex systems (in communication or transport…
Process Mining offers a powerful framework for uncovering, analyzing, and optimizing real-world business processes. Petri nets provide a versatile means of modeling process behavior. However, traditional methods often struggle to…