Give a formal definition of a DFA whose language is L1 w 01

Give a formal definition of a DFA whose language is L_1 = {w {0,1,2}*: the first character of w is the same as the last character of w}. (Think about what to do with the empty string and with strings of length 1.)

Solution

DFA Formal Definition (reminder) A deterministic finite automaton (DFA) is a 5-tuple. (Q,, , q0,F), where. Q is a finite set called the states, is a finite set called the alphabet, : Q × Q is the transition function, q0 Q is the start state, and F Q is the set of accept states.