The development of quantum software applications requires models capable to describe quantum features (superposition, entanglement, reversibility etc.) as well as the software algorithm requirements. The newly proposed Quantum Petri Nets (QPNs) have the structure of the classical Petri Nets (PNs), but their tokens represent superposed quantum states fulfilling the Hilbert space features. Instead of the integer numerical values of the PN marking, QPNs use quantum marking describing an extreme huge space. New conditions for the transition enabling and new mappings for the transition executions are conceived. A PN based language is used for the structure analysis. Replacing the classical tokens with the probability distribution of the quantum vectors, the QPN simulation is possible as well as the construction of a reachability graph.

Many software applications in the domains of reactive systems, cyber-physical systems, internet of things etc. need models that are capable to describe complex structure, concurrent behaviors including reaction to internal and external events, or distributed processing concerning task migration and cooperation. The newly proposed models called Object Enhanced Time Petri Nets (OETpNs) extend the classical Petri nets with tokens representing objects that implement data and tasks. Any task can be modeled by an OETPN, so in their turn some tokens can be OETPNs too. This leads to construction of OETPNs that include and move other OETPNs, all of them being capable to intercommunicate. They can take (receive) information from or send information to their environment. Allowing the distributed implementation, OETPN models can implement the information transfer and the task migration. The conceived models can describe the object dynamical creation and destruction. Some transition guards and mappings are used to control the flow of the executions, to assess the model states and to implement the information transformation. All the OETPN places have assigned types that allow the setting of passive or active objects. An algorithm to execute the OETPN models is provided with some examples of application for concurrent distributed developments.

Evolutionary systems (ES) include software applications that solve problems using heuristic methods instead of the deterministic ones. The classical computing used for ES development involves random methods to improve different kinds of genomes. The mappings of these genomes lead to individuals that correspond to the searched solutions. The individual evaluations by simulations serve for the improvement of their genotypes. Quantum computations, unlike the classical computations, can describe and simulate a large set of individuals simultaneously. This feature is used to diminish the time for finding the solutions. Quantum Petri Nets (QPNs) can model dynamical systems with probabilistic features that make them appropriate for the development of ES. Some examples of ES applications using the QPNs are given to show the benefits of the current approach. The current research solves quantum evolutionary problems using quantum genetic algorithms conceived and improved based on QPN. They were tested on a dynamic system using a Quantum Discrete Controlled Walker (QDCW).

Nowadays the world demands trains that go with a very high speed. To achieve this, a concept of a railway modeling using software applications is proposed for the purpose of increasing the resilience of railway traffic. Software applications need models that can describe their structure, reaction to internal and external events concerning cooperation and task migration. The behavior of the system which contains these types of trains can be conceived using OETPN (Object Enhanced Time Petri Nets). In this model, the tokens are active or passive objects. The active objects are sub OETPN that are executed by another thread of execution. In this model, the OETPNs are capable of communicating with each other via communication channels, they can send passive and active objects (i.e. task migration). Concurrency, reaction to internal or external events, synchronization and temporal behavior with fix and dynamic delays could be easily modeled using OETPN. A model for the railway system is proposed in this paper, the station, the controller and the software train are modeled using OETPN. The software train is an active object (a task, or an agent) that is moved inside the station model, meanwhile the physical train is moved on the physical infrastructure. The experiments of OETPN models successfully show that they can be used to solve the railway traffic problems due to their capabilities to adapt to the changing environment.

Object Enhanced Time Petri Nets (OETPN) can be used for specifications analysis, design (including synthesis), implementation, integration and maintenance of software applications in the domain of reactive systems, cyber-physical systems, embedded systems, real-time systems, internet of things etc. due to their ability to describe complex structures, concurrent behavior, reaction to the environment events, distributed processing, and task migration. OETPNs are extended from classical Petri Nets (PNs) by having tokens modeling passive and active objects (threads of executions). The system behavior is determined by a number of guards and mappings associated with each transition. In order to verify systems that are developed with OETPNs, Time Petri Nets (TPNs) are used with the clock-stamped state class (CS-class) technique. A new method for converting OETPNs to TPNs is proposed so that the reachability graph can be generated and computed the end- to- end time for each thread aside. A complete system analysis, implementation, and verification is provided for a synchronous and asynchronous approach for the real-time point of view.

While UML can describe all kinds of features by making use of the appropriate model (diagram), OETPN uses only one model for specification, synthesis, design, implementation, and finally verification and testing of components. The paper shows the equivalence between UML diagrams and their corresponding OETPN models. The guard conditions and mappings are indicated. As an example, the urban vehicle traffic problem is considered and activity, object communication and state machine diagrams are observed.