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1) Design an NFA with no more than $5$ states for: $$L_1 = \left \{aba b^n \mid n \geq 0 \right \} \cup \left \{ ab a^n \mid n\geq 0 \right \}$$

2) Design an NFA with $3$ states for: $$L_2= \left \{a^n \mid n \geq 1 \right\} \cup \left \{ b^m a^k \mid m,k \geq 0\right \}$$

3) Design an NFA with $4$ states for: $$L_3= \left \{ a^n \mid n\geq 0 \right \} \cup \left \{b^n a \mid n \geq 1 \right \}$$

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The NFA's for the given languages :

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rohankrishan asked Jun 29, 2022
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Example: 11110100000111 should be accepted. There are 6 zeros. 6 is divisble by 2 and 3. This machine required at least six states.
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