Automata Theory: Give both a CFG and a PDA recognizing each of the following languages over = {0, 1}: (Note that you cannot use the procedure given in Theorem 2.20 to design the PDA).

{w : the number of 0s equals the number of 1s}

{w : the number of 0s is less than the number of 1s}

{w : the number of 0s does not equal the number of 1s}

{0ⁿ1^m 0ⁿ : n, m 0}

{0ⁿ1^m : n, m 0 and n != m}

{0ⁿ1^m0^m1ⁿ : n, m 0}

{w : the number of 0s equals twice the number of 1s}

{w : w w^R}