Is the RE and the finite automata same?

Question

I want to understand if RE a∗ba∗ab∗ is same as the following the finite automata. The Part where I am confused is that, From state 3 to state 4 , there is ab , which means that the language needs to have ab at the end , while the RE just has b* which means 0 or more b . If not what is correct finite automata for this RE ?

Answer 1

Indeed, the regular expression a*ba*ab* is not equivalent to the DFA shown for exactly the reason you stated in your question.

Thompson's algorithm is a standard way of systematically converting a regular expression into an NFA. (If you need the finite automaton to be deterministic, you can then run the subset construction .)