Finite State Machines

You can check which strings are valid by tracing through the diagram. If a string does not end in an accept state (in this problem, S4), it cannot be generated by this FSM. This means that any string that can be generated by this machine must end with a C or a B since only C and B enter the accept state.

Strings in this machine can not end with a d

Since F is the accepted state, S4, d brings us to s3 which is unaccepted.

After entering final state S4, you can either go to S3 and then back to S4 or to S1

Since you must end in the accepting state, S4, it is not possible to end on the transition d, which leads to S3.

after reaching s4 via c going to s3 vid d is impossible

Since the question asks which string will not pass, the fastest way to solve this question is by making note of the last symbols of the proposed 4 answers.

You see one that ends on a d which does not lead to the final state.

last letter can't be anything except b or d

Here S1 is the entering state and S4 is the acceptable state. If we start following a string from S1 and end on S4 then that string can be generated by the DFA. This is because if we follow a string we should end on an acceptable state. Hence 1st, 2nd, 3rd are the generated string and 4th is the answer.

Due to S4 being the accepted state, the end result of a string should either be a 'B' or a 'C', because all of the strings end in 'C' with the exception of one ending in 'D' it was clear that the string ending in 'D' is a string that this FSM would not be able to compute.

Since S4 is the accept state, the string must end with C or B in order for the FSM to generate it successfully.

The S4 a.k. accept state (cause it's a double circle) is accepting c/b as a final input (look at the incoming arrow from S3&S2) ... so it won't end with an 'a' or 'd' ... all the string that will be generated guaranteed ended with 'b' or 'c' ... sorry for the grammar, english is not my main language :)

No link with "d" brings the state in S4, so if a string ends with "d" will never be accepted.