Exam Question - language recognizition I was at the Math-exam yesterday, and I am a bit unsure, if i solved a math problem correctly.
The question was something like this: 

Draw a automata that recognise the following language:
  $$ L = \{w : (0 | 1)^* \text{and } w \text{ ends with } 00 \} $$

See the image below where $q_3$ is the accept-state.


Your automaton should not accept the string $1001$. It needs transitions $(q_3,0)\rightarrow q_3$ and $(q_3,1) \rightarrow q_1$. 
