Integrated Structure and Semantics for Reo Connectors and Petri Nets

TL;DR

This paper develops an integrated model combining structure and semantics for Reo connectors and Petri nets, enabling direct comparison and application to dynamic reconfiguration through categorical formalization.

Contribution

It introduces a unified categorical framework for Reo connectors and Petri nets, facilitating their comparison and dynamic reconfiguration modeling.

Findings

Formal categorical model for connectors and Petri nets.

Semantic preservation through functorial mapping.

Application to dynamic reconfiguration via graph transformations.

Abstract

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation.