A Generalized Kahn Principle for Abstract Asynchronous Networks

TL;DR

This paper extends the Kahn Principle to a broad class of abstract asynchronous networks, providing a unified theoretical framework for understanding concurrent computation models, including non-deterministic systems and event-structure-based networks.

Contribution

It formulates a generalized Kahn Principle applicable to diverse asynchronous network models and proves its validity under natural assumptions, broadening the theoretical foundation of concurrent computation.

Findings

The generalized Kahn Principle applies to non-deterministic systems.

Models over arbitrary event structures satisfy the generalized Kahn Principle.

The framework unifies dataflow networks and more complex asynchronous models.

Abstract

Our general motivation is to answer the question: "What is a model of concurrent computation?". As a preliminary exercise, we study dataflow networks. We develop a very general notion of model for asynchronous networks. The "Kahn Principle", which states that a network built from functional nodes is the least fixpoint of a system of equations associated with the network, has become a benchmark for the formal study of dataflow networks. We formulate a generalized version of the Kahn Principle, which applies to a large class of non-deterministic systems, in the setting of abstract asynchronous networks; and prove that the Kahn Principle holds under certain natural assumptions on the model. We also show that a class of models, which represent networks that compute over arbitrary event structures, generalizing dataflow networks which compute over streams, satisfy these assumptions.