Final answer:
The NFA for the language B is constructed using three states and transitions based on the input characters '0' and '1'. State q2 is the accepting state. The automaton allows for the recognition of arbitrary concatenations of '10' and '101'.
Step-by-step explanation:
Non-deterministic Finite Automaton for Language B
The given language B is defined over the alphabet S = {0,1} where B consists of strings formed by concatenating elements from the set {10, 101}. To create a non-deterministic finite automaton (NFA) with L(N) = B using three states, we can consider the following transitions:
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- From the initial state q0, on input '1' we can transition to state q1.
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- From state q1, we can transition to state q2 on input '0', completing the sequence for '10'.
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- From state q2, we remain in q2 on input '0' to allow the concatenation of another '10'.
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- Alternatively, from state q2, on input '1' we transition back to q1 to start forming '101'.
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- State q2 is the accepting state as it ends the patterns of '10' or '101'.
The NFA has transitions labeled only with '0' or '1', and incorporates non-determinism allowing for transition to multiple states with the same input from q2.