Generalised Dining Philosophers as Feedback Control
This work addresses concurrency and resource allocation challenges in distributed systems, offering a formal and modular approach that is incremental in its application of existing control concepts.
The authors tackled the Generalised Dining Philosophers problem by applying feedback control theory, resulting in a modular solution that simplifies design and correctness proofs for three variants (N=1, centralized, and distributed).
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.