PETRI NETS

The purpose of this chapter is to give an overview of some currently active topics in automata and language theory. The overview is by no means intended to be exhaustive: Some topics have been entirely omitted, and the material within the topics presented has been chosen to give only a general idea of most representative notions and results. As the title of this chapter indicates, the attention is restricted to topics in automata and language theory.

The style of presentation in this chapter is somewhat different from that used in the previous chapters. Most of the proofs are either omitted or only outlined. Sometimes notions are introduced in a not entirely rigorous manner, and results are presented in a descriptive way rather than in the form of precise mathematical statements. We begin with a discussion of Petri nets.

In a customary model for computing, the notion of a state is quite essential. This is certainly true of most of the models discussed earlier. The notion of a state introduces, at least implicitly, a specific discrete linear time scale for all considerations involved: Time instants can be identified with the current states. Such a linear time scale is not desirable in all considerations. For instance, we might want to model systems where many processors operate independently and in parallel and where some partial computations depend (perhaps in a complicated way) on the outcome of some other computations.