Generalised Dining Philosophers as Feedback Control

TL;DR

This paper applies feedback control principles to the Generalised Dining Philosophers problem, developing a modular, formal solution architecture that simplifies design and correctness verification across different problem variants.

Contribution

It introduces a modular, formal framework for solving the Generalised Dining Philosophers problem using system composition and feedback control, enhancing clarity and correctness.

Findings

Modular solution architecture simplifies problem-solving.

Feedback controllers effectively address different problem variants.

Formal reasoning ensures correctness of the solutions.

Abstract

We revisit the Generalised Dining Philosophers problem through the perspective of feedback control. The result is a modular development of the solution using the notions of system and system composition (the latter due to Tabuada) in a formal setting that employs simple equational reasoning. The modular approach separates the solution architecture from the algorithmic minutiae and has the benefit of simplifying the design and correctness proofs. Three variants of the problem are considered: N=1, and N>1 with centralised and distributed topology. The base case (N=1) reveals important insights into the problem specification and the architecture of the solution. In each case, solving the Generalised Dining Philosophers reduces to designing an appropriate feedback controller.