Finite Automata limitations

[drwho]

I am trying to clear something that seems to be a little misleading for me.

 

I know the language over {a,b} consisting of all words containing the same number of occurrences of

the symbol a as of the symbol b is not regular.

 

I know that the language L over {a,b} consisting of all words containing

the same number of occurrences of ab as a substring as occurrences of ba as a substring

actually is regular.

 

What would be the best way to prove this? by finding a finite automaton that accepts this language?

[glitch]

try using pumping lemma theorem to prove it is regular. its much easier as you can handle it as a regular expression itself

Edited December 24, 2010 by glitch