Ullman (TOC) Edition 3 Exercise 3.2 Question 1 (Page No. 107)

Question

Here is a transition table for a DFA$:$

 

1. Give all the regular expressions $R_{ij}^{0}.$ Note$:$Think of state $q_{i}$ as if it were the state with integer number $i.$
2.  Give all the regular expressions $R_{ij}^{1}.$ Try to simplify the expressions as much as possible.
3. Give all the regular expressions $R_{ij}^{2}.$ Try to simplify the expressions as much as possible.
4. Give a regular expression for the language of the automaton.
5. Construct the transition diagram for the DFA and give a regular expression for its language by eliminating state $q_{2}.$