Here is an informal description how a DFA operates. An input to a DFA can be any string . Put a pointer to the start state q. Read the input string w from left to right, one symbol at a time, moving the pointer according to the transition function, . If the next symbol of w is a and the pointer is on state p, move the pointer to . When the end of the input string w is encountered, the pointer is on some state, r. The string is said to be accepted by the DFA if and rejected if . Note that there is no formal mechanism for moving the pointer.

A language is said to be regular if L = L(M) for some DFA M.