Q5 [20 pts] Design a PDA to accept each of the following languages. You may use either PDAs that accept by final state or ones that accept by empty stack, whichever is more convenient.

a) The set of all binary strings with more 1's than 0's.

b) The ternary language in Q1(a). For each PDA, please show the transition diagram instead of a sequence of transitions. (Q1 (a) [5 pts] Construct a CFG for the set of all binary strings of the form 0^i 1^j 0^k, where i+k = j.)