A starvation-free solution of the dining philosophers' problem by use of interaction systems

Abstract

For an independent and graphical representation of the constraints in distributed system parts the formalism of Loosely Coupled Systems (LCS) is recalled. The events in these structures are formally derived from symmetrical local restrictions. How the interaction between neighbour parts influences processes in these parts is then adequately described by a symmetrical transitional structure (slack of behaviour) in each part. In order also to represent further types of influence local excitement relations are introduced by means of which we can determine directions for processes in system parts and force them to leave a given local state. The formally extended system structures are called Interaction Systems (IS). — A solution of the Dining Philosophers' Problem recently given by Dijkstra [3] is briefly discussed. In order to demonstrate the flexibility and representational power of our graphical structures we then derive a starvation-free solution for that problem in a stepwise procedure. We do not assume a global finite-delay property.