Why is {a^nb^n | n >= 0} not regular?
computer-science, fsm, regular-language
Solution
What you're looking for is Pumping lemma for regular languages.
Here is an example with your exact problem:
Examples: Let L = {ambm | m ≥ 1}. Then L is not regular. Proof: Let n be as in Pumping Lemma. Let w = anbn. Let w = xyz be as in Pumping Lemma. Thus, xy2z ∈ L, however, xy2z contains more a’s than b’s.
Problem
In a CS course I'm taking there is an example of a language that is not regular: ``` {a^nb^n | n >= 0} ``` I can understand that it is not regular since no Finite State Automaton/Machine can be written that validates and accepts this input since it lacks a memory component. (Please correct me if I'm wrong) The wikipedia entry on Regular Language also lists this example, but does not provide a (mathematical) proof why it is not regular. Can anyone enlighten me on this and provide proof for this, or point me too a good resource?