What is the benefit of minimizing a finite automata?

Question

Minimizing a discrete finite automata is a standard problem in computer science. What are the benefits of minimizing a finite automata? Is it just an academic problem?

Answer 1

The principal reason to minimize a finite automaton is to save the implementation cost. When finite automata were being studied, it was with respect to the machines that implemented the function being studied. When an inverter or gate or memory component consisted of one or more vacuum tubes, http://en.wikipedia.org/wiki/Vacuum_tube - devices that cost money, consumed power and took up considerable space, you really, really wanted to reduce the number of tubes and the connections between them.

Even with the move to solid state implementations, real estate was often a concern. If a particular finite automaton was reused frequently in a system, optimizing the FA paid big dividends in chip yields.

Answer 2

minimized automata always preferable: (1) efficient(same algorithm if you apply on minimized automate) (2a) need less elements to implement (2b) smaller in size (2c) cheaper (3) sometime obvious to answer(redundant states may be reason of unnecessary complexity)