The Decent Philosophers: An Exercise in Concurrent Behaviour

Concurrent runs reveal more insight into distributed systems than interleaved runs. This is shown by help of Dijkstra’s paradigm of five philosophers. 1. The problem Antoni Mazurkiewicz’ seminal work on traces boosted the acceptance of Carl Adam Petri’s idea to conceive a single run (behaviour) of a distributed system not as a sequence of global states and steps, totally ordered in time, but as a set of local state and action occurrences, partially ordered by the cause effect relation. This paper is an exercise in this kind of runs, called concurrent runs in the sequel. This exercise is based on Dijkstra’s paradigm of dining philosophers as first introduced in [1]. Dijkstra never appreciated concurrent runs nor Petri Nets. But his paradigm nevertheless has interesting aspects to be nicely discussed in the framework of distributed runs and Petri Nets. As the reader probably remembers, the dining philosophers paradigm is about processes that share resources, with “philosophers” and “forks” to represent processes and resources, respectively. Dijkstra describes the philosophers system in [1] as follows: “Five philosophers, numbered from 0 to 4, are living in a house where the table is laid for them, each philosopher having his own place at the table. Their only problem – besides those of philosophy – is that the dish served is a very difficult kind of spaghetti, that has to be eaten with two forks. There are two forks next to each plate, so that presents no difficulty, as consequence, however, no neighbors may be eating simultaneously.” ∗Address for correspondence: Humboldt-Universität zu Berlin, Institute of Informatics, Unter den Linden 6, 10099 Berlin, Germany 2 W. Reisig / The Decent Philosophers Ep At