Related papers: Reversing Place Transition Nets
Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high…
Unfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings…
Recently introduced Petri net-based formalisms advocate the importance of proper representation and management of case objects as well as their co-evolution. In this work we build on top of one of such formalisms and introduce the notion of…
In process discovery, the goal is to find, for a given event log, the model describing the underlying process. While process models can be represented in a variety of ways, Petri nets form a theoretically well-explored description language…
Process models are, like event data, first-class citizens in most process mining approaches. Several process modeling formalisms have been proposed and used, e.g., Petri nets, BPMN, and process trees. Despite their frequent use, little…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
Uniform coloured Petri nets can be abstracted to their skeleton, the place/transition net that simply turns the coloured tokens into black tokens. A coloured net and its skeleton are related by a net morphism. For the application of the…
The time complexity of the presented in 2013 by the author small universal Petri nets with the pairs of places/transitions numbers (14,42) and (14,29) was estimated as exponential. In the present paper, it is shown, that their slight…
Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed…
Place bisimilarity $\sim_p$ is a behavioral equivalence for finite Petri nets, originally proposed in \cite{ABS91}, that, differently from all the other behavioral relations proposed so far, is not defined over the markings of a finite net,…
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…
Reversible architectures have been shown to be capable of performing on par with their non-reversible architectures, being applied in deep learning for memory savings and generative modeling. In this work, we show how reversible…
Detectability describes the property of a system whose current and the subsequent states can be uniquely determined after a finite number of observations. In this paper, we developed a novel approach to verifying strong detectability and…
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…
Time-Basic Petri nets, is a powerful formalism for modeling real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We…
Concurrency and probability are both much studied extensions of sequential computation. Within concurrency theory, there is a broad divide between interleaving models and logics, which model concurrency by non-determinism, and `truly…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems…
The theory of Petri Nets provides a general framework to specify the behaviors of real-time reactive systems and Time Petri Nets were introduced to take also temporal specifications into account. We present in this paper a forward…
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…