' \ufeffUse the closure properties to find NFA that accepts the…

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Anu Bhardwaj · Accepted Answer

To construct an NFA for the language L = ( a b ∗ a a + b ( b a ) ∗ ) L = (ab^*aa + b(ba)^*) , we can follow similar steps as before, using closure properties to combine simpler NFAs. a b ∗ a a ab^*aa This part of the language matches strings that start with 'a', followed by zero or more 'b's, and end with 'aa'. The regular expression for this part is a b ∗ a a ab^*aa The corresponding NFA for this part can be constructed as follows: b ( b a ) ∗ b(ba)^* This part of the language matches strings that start with 'b' and are followed by zero or more occurrences of 'ba'. The regular expression for this part is b ( b a ) ∗ b(ba)^* . The corresponding NFA for this part can be constructed as follows: Combined NFA : Combine the NFAs for a b ∗ a a ab^*aa  and b ( b a ) ∗ b(ba)^*  into a single NFA. Add a new initial state q s q_s ​ and ε-transitions from q s q_s  to the initial states of both NFAs. Make the initial states of both NFAs non-initial. Make the final states of both NFAs non-final and add ε-transitions from their original final states to a new final state q f q_f q f ​ . Putting it all together, the combined NFA looks like this: Initial state: q s q_s ​ The transition from q s q_s to initial states of both NFAs with ε-transitions. States for a b ∗ a a ab^*aa : q 0 , q 1 , q 2 q_0, q_1, q_2 (with transitions as described earlier). States for b ( b a ) ∗ b(ba)^* : r 0 , r 1 , r 2 r_0, r_1, r_2 ​ (with transitions as described earlier). Final state: q f q_f q f ​ Add ε-transitions from the final states of both NFAs to q f q_f q f ​ . This NFA will accept strings that match either a b ∗ a a ab^*aa a b ∗ aa or b ( b a ) ∗ b(ba)^* b ( ba ) ∗ , as required by the language L L L . Final answer ;- Here's the final NFA for the language L = ( a b ∗ a a + b ( b a ) ∗ ) L = (ab^*aa + b(ba)^*) Initial state: q s q_s ​ Transitions: From q s q_s with 'ε' to q 0 q_0 ​ (start of a b ∗ a a ab^*aa a b ∗ aa part) and to r 0 r_0 ​ (start of b ( b a ) ∗ b(ba)^* part). a b ∗ a a ab^*aa  part transitions: q 0 q_0  to q 1 q_1  with 'a'. q 1 q_1 ​ to q 2 q_2 ​ with 'a'. q 2 q_2 ​ loops to itself with 'b'. q 2 q_2  loops to itself with 'a'. b ( b a ) ∗ b(ba)^*  part transitions: r 0 r_0 ​ to r 1 r_1 ​ with 'b'. r 1 r_1  to r 2 r_2 ​ with 'b'. r 2 r_2 ​ loops to itself with 'b'. r 2 r_2 ​ to r 3 r_3 ​ with 'a'. Final transitions: From q 2 q_2 ​ to q f q_f  (end of a b ∗ a a ab^*aa  part) with 'ε'. From r 3 r_3 ​ to q f q_f ​ (end of b ( b a ) ∗ b(ba)^*  part) with 'ε'. Final state: q f q_f ​ This NFA accepts strings that match either a b ∗ a a ab^*aa  or b ( b a ) ∗ b(ba)^* , as required by the language L L L .

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Anu Bhardwaj

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