I just went to read wikipedia to check a point on FA minimization, and I read there the following sentence:
The minimal DFA ensures minimal computational cost for tasks such as pattern matching.
I have tried to imagine how, but my feeling is that DFA minimization reduces the size of the program, which is especially important when it is hardware, but will hardly do anything to speed up the computation (well, indexing states might be easier when there are less states, depending on computation model, but this seems far fetched).
Of course, from an abstract logical point of view, a minimal DFA does ensure minimal computational cost, when that same cost is ensured by any DFA for the language.
Am I missing a point? Which?