pumping lemma help!

[cwarrior]

Can somebody help me understand how the pumping lemma works?
I am having a hard time understanding it. Like i have seen examples and definitions but i just get lost and it doesn't get through my head.

[Brightguy]

Well, you might have to be a little more specific, but I'll try to give you a high-level flavour.

Let L be a regular language. The pumping lemma says that any really long word in L can be split into three parts such that the middle part can be duplicated as many times as you want and the new word is still in L.

So if w is a sufficiently long word in L then there is some decomposition w=xyz (x, y, z are strings and y is not empty) so that xyyz, xyyyz, xyyyyz, xyyyyyz, etc. are also in L (and xz too).

You can also strengthen that statement and say that in the xyz decomposition the string xy can't be too long.

This makes sense if you consider finite automaton. Since they have a finite number of states, a state must be repeated during the processing of any string with more symbols than there are states in the automaton. And if you were able to get a DFA to repeat a state once you can get it to repeat as many times as you want by feeding it the same symbols that got it to repeat the first time.