What is the benefit of minimizing a finite automata?

Question

Minimizing a discrete finite automata is astandard 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

最小化自动机总是可取的：（1）高效（如果在最小化自动上应用相同的算法）（2a）需要较少的元素来实现（2b）较小的尺寸（2c）便宜（3）有时很明显可以回答（冗余状态可能是原因不必要的复杂性）

Answer 3

Minimization of a finite automata helps in reducing the compile time, as it removes identical operations.

When we minimize an expression,we tend to remove the unused states or we merge two or more states into a single equivalent state which are likely to produce same output. Merging states like this should produce a smaller automaton that accomplishes exactly the same task as our original one. (Here the unreachable states are removed and the states are checked whether they are distinguishable or not. If undistinguishable the states are merged else the states are uniquely represented).

As it reduces the compilation time,results in increasing the processing speed of the program. Running a program which can run a second or two faster than other programs, can vastly increase the scope of the program. Therefore minimization is very essential in the process.

Answer 4

First of all, minimization of a finite automata is very useful in making the compilers execute faster, as it removes identical operations.

When we minimize an expression, we merge two or more states into a single equivalent state.

Merging states like this should produce a smaller automaton that accomplishes exactly the same task as our original one.

This is very much required to reduce the whole total compilation time and eventually increase the processing speed of the program.

Running a program which can run a second or two faster than other programs, can vastly increase the scope of the program.

Therefore minimization is very essential in the process.