Automatic creation of exercises

[heatherleaf]

It should be possible to auto-create exercises of a given difficulty level. The difficulty can be something like:

• (simple) the length of the shortest solution
• (complex) the probability of finding the correct solution by randomly selecting menu items (this can increase if there are several paths to find a solution)

[heatherleaf]

We can divide this problem into two subproblems:

1. If the goal sentence is known, can the system suggest the start sentence?

   • do a random walk from the start sentence,
 performing N random moves (where N is given)
   • make sure there is no shorter path to the goal

2. Can the system also suggest the goal sentence?

   • generate random text from the lesson grammar
   • probabilities can be learned from a corpus

These suggestions will probably not be perfect, so we should treat them as suggestions, and let the teacher decide and possibly modify.

[heatherleaf]

Depends on #58