Virtual Labs

Given the regular expression (a|b)*c, what is the accepting condition of the NFA built using Thompson’s Construction?

a: It accepts only the sequence 'abc'. Explanation

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b: It accepts any sequence (including empty) of 'a' and 'b' followed by a single 'c'. Explanation

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c: It accepts strings where 'c' can appear anywhere in the middle. Explanation

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d: It accepts only repetitions of 'c'. Explanation

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In Thompson’s Construction, how are ε-transitions specifically used during the concatenation of two fragments R1 and R2?

a: The final state of R1 is connected to the start state of R2 using an ε-transition. Explanation

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b: The start state of R1 is merged with the start state of R2. Explanation

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c: All transitions of R1 are replaced by ε-transitions leading into R2. Explanation

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d: Both fragments are duplicated to avoid nondeterminism. Explanation

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When applying the Kleene star (*) to an NFA fragment, which of the following structural modifications is correct?

a: Introduce a new start and accept state, connect start → fragment start and fragment accept → new accept using ε, and add a loop from fragment accept → fragment start. Explanation

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b: Replace all input symbols with ε to allow skipping transitions. Explanation

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c: Manually duplicate the fragment infinitely to represent repetitions. Explanation

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d: Remove the accept state and treat the start as both start and accept. Explanation

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Which step in the subset construction algorithm requires computing the ε-closure of a state set?

a: When determining the initial DFA state from the NFA start state. Explanation

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b: Only when finalizing the DFA transition table. Explanation

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c: Only when processing union operations in the original regex. Explanation

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d: At the end of the algorithm to minimize states. Explanation

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For the regex (a|b)*abb, what is the correct order of operations in Thompson’s Construction?

a: First build union (a|b), apply Kleene star, then concatenate with 'a', 'b', 'b'. Explanation

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b: First concatenate 'a', 'b', 'b', then apply Kleene star, then union. Explanation

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c: Apply Kleene star to each symbol individually before concatenating. Explanation

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d: Directly construct NFA without breaking the regex. Explanation

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Why is Thompson’s Construction widely preferred in regex engine implementation?

a: It guarantees the minimum possible number of states in the NFA. Explanation

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b: It provides a systematic, mechanical way to build NFAs for any regex using only small fragment rules. Explanation

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c: It eliminates nondeterminism completely at the construction stage. Explanation

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d: It works only for finite-length regular expressions. Explanation

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Conversion of RE to NFA