How do a DFA Process Strings?

The important thing about DFA is to know that it identifies the acceptance of strings. 

The language of the DFA is the set of all strings that the DFA accepts. 

Assume that S1, S2, S3, ….. Sn is a sequence of input symbols. 

q0 is the starting states of DFA

Then first we shall check the transition δ (q0, S1) = q1 where q1 is the state where DFA reaches from q0 by input of S1 where DFA reaches from q0 by input. Then we apply δ(qi-1, Si) = qi for each i.

If qn ∈ F then the input S1, S2, S3, ….. Sn is accepted otherwise the string is rejected. 

For example, 

Consider the DFA that identifies whether the given decimal is even or odd. 

Here we consider 3 states, one start state qstart, one even state qeven and one odd state qodd. 

If the machine stops at qeven the given number is even. 

If it stops at qodd the given number is odd.