Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri’s general systems theory and have very different interpretations, ranging from Einstein’s relativity theory to elementary information processing gates. Despite their simple definitions, their properties are still not completely understood. This contribution provides for the first time a formal definition together with new results concerning their structure. Cycloids are proved to be live and safe. It is shown that the minimal length of a cycle is the length of a local basic circuit, possibly decreased by an integer multiple of the number of semi-active transitions. These results allow to find the defining parameters of a cycloid from the static properties of the net system. Similar results are obtained for degenerate cycloids.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.