Often you can find that finite automata (whether it be DFAs or NFAs) often can be used to craft a combinatorial algorithm that can be used to exhaust the finite language.  Come up with a really refined NFA, maybe you can find its counterpart in exhaustive algorithms.  I know I have looked a bit into this with context-free grammars (CFGs), but I would suspect the same could be done with NFAs---especially if lengths of sequences are things you want to vary in a more specific manner (though you can do that all with CFGs).  That's one way you could use them not in compiler design.  Keep in mind that these are simple computational models, so when you design one with a specific  language they will have counterparts as pseudocode when you develop an algorithm if you use the same structure.  There's a correspondence.  That's one reason why these models are very important in Theoretical Computer Science. 

The problems of management automated in the enterprises, can be solved surely by these models with hypotheses a lot of restrectives or with conditions to the limits.

In the automated management, the research of the strategies to optimize the time

or to optimize the energy is a fundamental question.

It is about determining an optimal order corresponding to an optimal trajectory

or to an optimal energy or at one optimal time.

A simple example in the industry is the management of the train.

One can determine the strategies to minimize the energy spent by the train in a journey.

One can also minimize the length of a journey.

Optimization of a system (train) in movement.

Several examples can be observed in the industry.