a DFA that recognizes the string 'a':

    (s0)- a ->(s1)      
    
    
    an NFA with epsilon transitions that recognizes
    the string 'a*':
    
                 +-->(s1)- a ->(s2)- e -+
                 |                      |
    +-->(s0)- e -+----------------------+-->(s3)- e -+
    |                                                |
    +------------------------------------------------+