Detection of Deadlocks in an Infinite Family of Nets

In this paper, we introduce a particular model of massively parallel net, made of the connexions of identical patterns. As a matter of fact, one can construct in a modular way an infinite family of nets from a given pattern. In this framework, we raise an entirely original class of problems : prove that, for any such net, whatever the execution is, some properties are verified and some other are not. The originality (and the difficulty) comes from the fact that the family of nets is infinite. We give a method for validating a pattern with respect to the deadlock problem. If a pattern is valid, then any net, constructed by connecting an arbitrary number of patterns in an arbitrary way, is deadlock-free.