Automata

Explicit construction like "on state p, when read a, the top of stack is b, the next move is to ...." Psuedo-code in the form of or instructions 1. Construct a DPDA (yes, deterministic DPA) to accept language [0"13n n 2 11. You need write down the explicit construction. 2. Construct a PDA to accept language {w E {0, 1}* : #0(w> #1 (w)). (It is fine you describe how your machine works in English.) 3. Construct a PDA to accept language L-{w E 10, 1)* : each prefix of w is in the language defined in Problem 2. ). You need also write down the explicit construction. (This is actually an easy problem. First, you have to understand the language. For instance 0001100111001 E L, but 001110 why? since w E L requires that each prefix of w contains more or the same number of 0's than 1's.)