Practice Question Language
Duration: 2 min
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The video features an educational lecture on automata theory, specifically analyzing a Finite Automaton (FA) labeled M. The instructor presents a state diagram with five states: S0, S1, S2, S3, and S4. The objective is to determine the language L(M) accepted by this machine from four given multiple-choice options. The instructor begins by tracing the transitions to understand the machine's behavior. He identifies that the sequence of transitions S0 -> S1 (on 'a'), S1 -> S2 (on 'a'), S2 -> S3 (on 'b'), and S3 -> S4 (on 'b') corresponds to the input string "aabb". State S4 is a final state, indicated by a double circle, and crucially, it has self-loops for both 'a' and 'b'. This means that once the machine reaches S4, it remains in the accepting state regardless of subsequent inputs.
The instructor then systematically evaluates the options. He notes that option (a) suggests words must start with "aabb". However, since S0 has a self-loop on 'b', a string like "baabb" would transition S0 -> S0 -> S1 -> S2 -> S3 -> S4, which is accepted. Thus, the word does not need to start with "aabb". He dismisses option (c) "ending with aabb" because the loops in S4 allow any characters to follow "aabb", so a string like "aabbba" is also accepted. Similarly, option (d) "exactly one occurrence" is rejected because the loops in S4 allow the machine to accept strings with multiple occurrences of "aabb", such as "aabbaabb". Finally, he concludes that option (b) "Set of all words having aabb as a sub word" is the correct description. The machine accepts any string that contains "aabb" as a substring, as reaching S4 guarantees acceptance. The instructor underlines option (b) to confirm the answer.
Chapters
0:00 – 1:36 00:00-01:36
The instructor introduces the problem of finding the language L(M) for the given machine M. He displays the state diagram with states S0 through S4. He traces the path for "aabb" (S0->S1->S2->S3->S4) and notes the final state S4 has loops on 'a' and 'b'. He discusses the options, eliminating (a) because S0 loops on 'b', eliminating (c) and (d) because S4 loops allow any suffix or multiple occurrences. He concludes that the machine accepts any word containing "aabb" as a substring, underlining option (b).
The lecture demonstrates how to analyze a Finite Automaton to determine its accepted language. By tracing paths and observing state transitions, particularly final states with self-loops, one can deduce that the machine accepts any string containing a specific substring. The key insight is that once the substring "aabb" is recognized, the machine enters a "trap" or "accepting" state that never leaves, effectively matching the language of strings containing that substring.