Theoretical Foundation of Colored Petri Net through an Analysis of their Markings as Multi-classification

TL;DR

This paper develops a theoretical framework connecting colored Petri nets to multi-classification systems, enabling analysis of evolving information flow in dynamic distributed systems using a classification-based approach.

Contribution

It extends classification theory to multiclassification and applies it to colored Petri nets, linking markings to multiclassification and constructing a knowledge base.

Findings

Markings of CPN are equivalent to multiclassification.

Unfolding multiclassification into binary classification facilitates theory computation.

Amalgamation of classifications from CPN markings forms a comprehensive knowledge base.

Abstract

Barwise and Seligman stated the first principle of information flow: "Information flow results from regularities in the distributed system." They represent a distributed system in terms of a classification consisting of a set of objects or tokens to be classified, a set of types used to classify tokens, and a binary relation between tokens and types that tells one which tokens are classified as being of which types. We aim to further this investigation and proceed with a dynamic or evolving system instead of a static system. We claim that a classification is a snapshot of a distributed system at a given moment or context. We then aim to answer the question posed by an evolving context. As the context or configuration changes, how to regularities evolve. This paper is a continuation of an investigation we started in \cite{esterlin}, where we initiated how to capture a dynamism of information flow with a Kripke structure. Here we develop the same procedure with colored Petri net(CPN). We first extend the classification concept to multiclassification by replacing its binary relation between tokens and types with a multi relation: a function from tok(A) x typ(A) to N, the set of natural numbers. The multiclassification will unfold into binary classification in order to compute its theory. It turns out that markings of a CPN are multiclassification; Amalgamating the theories of those classifications obtained as markings of CPN results in a CPN's knowledge base.