Pumping Lemma Homework

Use the pumping lemma to prove that the following languages are not regular.

In class I presented proof sketches of several examples. For this homework please write up full proofs similar to the format of the examples in the book. Turn in a hard copy in class.

  1. \(\{ \texttt{a}^m \texttt{b}^n \texttt{c}^{m+n} | m \ge 0\) and \(n \ge 0 \}\)
  2. \(\{ \texttt{a}^{2^n} | n \ge 0 \}\)