Modelling mutual exclusion algorithms

Abstract

Introduction In the previous chapters of this book, we have illustrated the use of the ingredients in our methodology for the description and analysis of reactive systems by means of simple but, it is hoped, illustrative examples. As we have mentioned repeatedly, the difficulty in understanding and reasoning reliably about even the simplest reactive systems has long been recognized. Apart from the intrinsic scientific and intellectual interest of a theory of reactive computation, this realization has served as a powerful motivation for the development of the theory we have presented so far and its associated verification techniques. In order to offer you further evidence for the usefulness of the theory you have learned so far in the modelling and analysis of reactive systems, we shall now use it to model and analyse some well-known mutual exclusion algorithms. These algorithms are amongst the most classic ones in the theory of concurrent algorithms and have been investigated by many authors using a variety of techniques; see, for instance, the classic papers Dijkstra (1965), Knuth (1966) and Lamport (1986). Here, they will give us the opportunity to introduce some modelling and verification techniques that have proved their worth in the analysis of many different kinds of reactive system. In order to illustrate concretely the steps that have to be taken in modelling and verification problems, we shall consider a very elegant solution to the mutual exclusion problem proposed by Peterson and discussed in Peterson and Silberschatz (1985).