On Reduction and Synthesis of Petri's Cycloids
This work addresses foundational issues in Petri net theory for researchers in formal methods and systems modeling, but it appears incremental as it builds on existing cycloid definitions.
The paper tackled the problem of analyzing and synthesizing cycloids, a class of Petri nets for modeling synchronized processes, by developing reduction systems and proving properties of irreducible cycloids, resulting in an efficient decision procedure for cycloid isomorphism.
Cycloids are particular Petri nets for modelling processes of actions and events, belonging to the fundaments of Petri's general systems theory. Defined by four parameters they provide an algebraic formalism to describe strongly synchronized sequential processes. To further investigate their structure, reduction systems of cycloids are defined in the style of rewriting systems and properties of irreducible cycloids are proved. In particular the synthesis of cycloid parameters from their Petri net structure is derived, leading to an efficient method for a decision procedure for cycloid isomorphism.