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

5.2. What would happen if the construction step for an NFA for the subexpression e* in Thompson's algorithm were defined as