On Reduction and Synthesis of Petri's Cycloids

TL;DR

This paper explores the structure of Petri's cycloids, introducing reduction systems and synthesis methods that enable efficient decision procedures for cycloid isomorphism, advancing Petri net modeling techniques.

Contribution

It presents a novel reduction system for cycloids and a synthesis method for parameters from Petri net structures, improving analysis and classification.

Findings

Defined reduction systems for cycloids

Proved properties of irreducible cycloids

Developed an efficient decision procedure for isomorphism

Abstract

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.