What are the limitations of finite automata?

Answer 1

The defining characteristic of FA is that they have only a finite number of states. Hence, a finite automata can only "count" (that is, maintain a counter, where different states correspond to different values of the counter) a finite number of input scenarios.

There is no finite automaton that recognizes these strings:

• The set of binary strings consisting of an equal number of 1's and 0's
• The set of strings over '(' and ')' that have "balanced" parentheses

The 'pumping lemma' can be used to prove that no such FA exists for these examples.