5. Regex to NFA to DFA conversions

5.1. Convert one of the following regular expressions to an NFA using Thompson's algorithm and then to a DFA using subset construction.

• $ (1 \cup \varepsilon)(0^*1)^*0^* $
• $ (0\cup 01) \cup 1(10^*)^* \cup \varepsilon $
• $ (((00 \cup 11)^*1)^*0)^* $

5.2. What would happen if the following construction steps for $ e_1e_2 $ and $ e^* $ in Thompson's algorithm were defined as follows?