Summary: We present a comprehensive introduction to the theory of Elementary Net (EN) systems, covering both their structure and behaviour. The chapter is organize as follows. It consists of eight sections, of which this is the first. The second section recalls some standard mathematical notions needed in this chapter. Section 3 is a basic introduction to EN systems, both informally and formally. It begins with an informal introduction of EN systems. This is followed by the formalization of the notion of a net which represents the structure of an EN system. It consists of places (i.e., local states) and transitions (i.e., local transitions), connected by the neighborhood relation. Then the dynamic execution of a net in both a sequential and a concurrent setting is discussed. An EN system is a net with an initial state, where all its executions begin. The sequential executions of the system that start from the initial state are called its firing sequences. Considering all states that are reachable by such a firing sequence leads to the state space of an EN system, formalized by the notion of a sequential configuration graph. The sequential configuration graph is extended to the (full) configuration graph of the system, in which also concurrent execution steps are represented. It is shown that the full configuration graph of an EN system is completely determined by its sequential configuration graph. Finally, we demonstrate how fundamental situations of concurrent systems can be naturally expressed in the model of EN systems.
For the entire collection see [Zbl 0903.00072].