Abstract Background Statecharts are diagrams comprised of visual elements that can improve the modeling of reactive system behaviors. They extend conventional state diagrams with the notions of hierarchy, concurrency and communication. However, when statecharts are considered to support the modeling of system interactions, e.g., in Systems of Systems (SoS), they lack the notions of multiplicity (of systems), and interactions and parallelism (among systems). Methods To solve these problems, this paper proposes extensions to statecharts. First, a notation to represent a set of orthogonal states, similar in their structures but belonging to different systems, like a pool of telephone systems, is proposed. Second, the concept of communication among parallel states is extended to also represent system interactions, i.e., the relationships among orthogonal systems by means of proper interaction mechanisms like event broadcast. Results The proposed extensions to statecharts are symbolic notations that result from an analogy with multi-layer Printed Circuit Boards (PCB). Systems are modeled as concurrent layers that can interact through circuit holes. The resulting diagrams are named pcb-statecharts. Skype-like systems are used to exemplify the modeling of system interactions. They are modeled as concurrent systems disposed in different layers that interact to enable conference calls. A discussion about the use of this notation to model systems of systems is also presented. Conclusions The main contribution of this paper is giving to system engineers additional support to model systems interactions. Multiple interacting systems can be designed with separation of concerns. Different viewpoints enable the modeling of these systems as both independent systems and members of a whole. The resulting diagrams improve the notions of multiplicity of systems, and concurrency and parallelism among systems. Additionally, the proposed symbolic notation enables the building of diagrams without the need of physically connecting related entities in the model.
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