Consider the following simplified algorithm to decide whether an FA with exactly N states has an empty language:
Step 1 Take the edges coming out of each final state and tum them into loops going back to the state they started from.
Step 2 Relabel all edges with the letter x. (We now have an NFA.)
Step 3 The original FA has a nonempty language if and only if this new NFA accepts the word X^N.
Illustrate this algorithm and prove it always works.
Is this an effective procedure?