Comprehension

A machine is represented by states Q, input alphabet Σ, transition function δ. Initial state qo and final state F. The machine accepts all the strings over Σ = {a,b}, which starts and ended with any combination of all alphabet and abb works/lies in all the strings to be accepted 

For the above mentioned passage which of the following is correct?

  1. qImage67a74bbab8840bd62b8ff38d
  2. qImage67a74bbbb8840bd62b8ff38e
  3. qImage67a74bbbb8840bd62b8ff38f
  4. qImage67a74bbcb8840bd62b8ff391

Answer (Detailed Solution Below)

Option 3 : qImage67a74bbbb8840bd62b8ff38f

Detailed Solution

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The correct answer is Option 3.

Key Points

Option 1: The DFA transitions a → b → b directly to final state. But it lacks proper looping logic to verify intermediate characters. No trap state. Incorrect.

Option 2: Accepts strings only if they end with “abb”. But the question states the string can have “abb” anywhere. Incorrect.

Option 3: The DFA clearly detects “abb” and loops over further inputs. So, even strings like “aabb”, “baabbab”, “abba” will be accepted. Correct ✔

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