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 outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category Open(Petri), which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category ${\mathbb O}$ pen(Petri). We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of ${\mathbb O}$ pen(Petri). The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.

Alveolar echinococcosis (AE) is a zoonotic parasitic diseases caused by a cestode parasite known as Echinococcus multilocularis. The parasite has a wildlife cycle with definitive hosts (foxes) and small mammals as intermediate hosts (rodents) while humans are the accidental hosts. Parasite infection pressure relation to time of the year and age dependent infection pressure for parasite abundance also depend on the urbanization. The aim of current work is forecasting the thresholds via the computational analysis of the disease spread which is a useful approach since it can help to design the experimental settings with better planning and efficiency. Network analysis when interlinked with the computational techniques provides better insight into the spatial and temporal heterogeneities. In the present study, a mathematical framework that describes the transmission dynamics and control measures of E. multilocularis in foxes is documented. We used treatment of foxes with baits for the prevention of the E. multilocularis infection. A novel approach of networking, called Petri net (PN), based on density dependent differential equations, is utilized during this research. The accurate description of the transmission of the parasite and the effect of drug on it is provided to the readers in this article. The transitions, which are difficult to analyse theoretically, are presented with the aid of the discrete approach of networking. A discrete mathematical framework can prove to be an accurate and robust tool to analyse and control the parasite dynamics.

The paper considers the highest control level organization of a flexible manufacturing cell (FMS). The indeterminancy problem in Petri nets is discussed as well as a method for overcoming it by two control levels. The net is decomposed into individual robot nets and machines. A simple language for defining robot activation conditions is developed and used for defining knowledge base contents. A method for linking it with other control modules is given. Also, the solution performance is analysed.

This paper describes the use of a hybrid system comprising a multi-layer perceptron and a Petri Net model to control the navigation of multiple mobile robots in an unknown and cluttered environment. The multi-layer perceptron is trained with examples representing the typical static obstacles to be encountered by the robots and the evasive actions to be taken. The Petri Net model embodies the rules describing how the robots should move in order to avoid colliding against one another. The hybrid system has been implemented in simulation software as well as in actual mobile robots. The paper presents the results of simulation and practical tests that demonstrate the ability of groups of robots incorporating the proposed navigation system to negotiate various types of obstacles and find targets successfully.

Processes in Place/Transition (P/T) nets are defined inductively by a peculiar numbering of place occurrences. Along with an associative sequential composition called catenation and a neutral process, a monoid of processes is obtained. The power algebra of this monoid contains all process languages with appropriate operations on them. Hence the problems of analysis and synthesis, analogous to those in the formal languages and automata theory, arise. Here, the analysis problem is: for a given P/T net with an initial marking find the set of all processes the net may evoke. The synthesis problem is: given a process language L decide if there exists a marked net whose evolutions (represented by processes) are collected in L and, in the positive case, find such net and its initial marking. The problems are posed and given a general solution.

This paper presents a novel knowledge-based Petri net approach to mechanical systems and assemblies modeling within a design with objects environment. A new unified class of object-oriented knowledge Petri nets, which can incorporate a knowledge-based system with ordinary Petri nets, is defined and used for the unified representations of assembly design and modeling. The object knowledge Petri nets, as a graphical language and a new knowledge-based description scheme, can be used to express the qualitative and quantitative aspects of the assembly design and modeling process in an interactive and integrated way. The four-level hierarchy model is proposed and constructed in terms of function-behaviors, structures, geometries, and features. The function-behavior-structure description is built on more abstract concepts so that it can match well top-down design. The static and dynamic characteristics in the design of assembly can also be captured. With the help of fuzzy logic, the incomplete, imprecise knowledge and uncertainty in the design process can also be dealt with. Therefore, the hybrid design object model can incorporate product data model, top-down design process, and assembly process model using an object-oriented, knowledge-based, feature-based, parametric, and constraint-based modeling approach, and can provide a more accurate and more flexible representation. To verify and demonstrate the effective use of the proposed hybrid design object model, a prototype system has been developed. This research provides a knowledge-intensive framework for intelligent assembly design and modeling.

The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note shows that the new condition stating that each transition is covered by a minimal closed support T-invariant, is necessary and sufficient for the existence of a solution for the traffic equations for batch routing queueing networks and stochastic Petri nets.