Using conventional reasoning techniques for self-organising systems

Self-organising systems have become important relatively recently. It is frequently claimed that their complex nature necessitates new formalisms to express and reason about them. In this paper the opposite view is taken. Following Back's use of action systems to express a distributed system as an initialised possibly nonterminating loop, here two simple but representative case studies of self-organising systems are explored using only conventional techniques. The first deals with the configuration of an ad hoc network and shows how safety and liveness can be accurately expressed with an initialised loop. The second involves, like many self-organising systems, probabilistic behaviour and it is shown that existing techniques suffice to establish the system behaviour. In conclusion, the techniques illustrated can be used to provide a higher level of assurance than is possible with simulation alone.