Suppose L is a regular language. Then there is an integer n so that for any x? L with |x|>=n, there are strings u, v, and w so that x=uvw |uv|<=n |v|>0 For any m>=0, uvm w ∈ L Application The pumping lemma is extremely useful in proving that certain sets are non-regular. The general methodology followed during its applications is Select a string z in the language L. Break the string z into x, y and z in accordance with the above conditions imposed by the pumping lemma. Now check if there is any contradiction to the pumping lemma for any value of i.
