On Reduction and Synthesis of Petri's Cycloids

TL;DR

This paper explores the structure of Petri's cycloids, providing reduction methods and a synthesis procedure for their parameters, enabling efficient decision procedures for cycloid isomorphism.

Contribution

It introduces a formal reduction system for cycloids and derives a synthesis method for parameters from Petri net structures, advancing their algebraic analysis.

Findings

Defined reduction systems for cycloids.

Proved properties of irreducible cycloids.

Developed an efficient decision procedure for cycloid 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.