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lfa:2023:lab09 [2023/12/11 23:26] mihai.udubasa |
lfa:2023:lab09 [2024/01/16 22:31] (current) alexandra.udrescu01 |
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**9.1.1.** $ L = \{\: w \in \{A,B\}^* \ | \:w \text{ is a palindrome}\} $. | **9.1.1.** $ L = \{\: w \in \{A,B\}^* \ | \:w \text{ is a palindrome}\} $. | ||
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{{ :lfa:2022:lfa2022_lab9_1_1.png?400 |}} | {{ :lfa:2022:lfa2022_lab9_1_1.png?400 |}} | ||
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We can either generate one ''a'' followed by one ''b'', as well as one ''b'' followed by one ''a''. At the same time, other sequences of equal number of a and b can appear freely, hence one solution is: | We can either generate one ''a'' followed by one ''b'', as well as one ''b'' followed by one ''a''. At the same time, other sequences of equal number of a and b can appear freely, hence one solution is: | ||
$math[S \leftarrow aSbS \mid bSaS \mid \epsilon] | $math[S \leftarrow aSbS \mid bSaS \mid \epsilon] | ||
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**Solution 2:** | **Solution 2:** | ||
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*-/ | *-/ | ||
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/-* | /-* | ||
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$ S \leftarrow aS | aaS | \epsilon $\\ | $ S \leftarrow aS | aaS | \epsilon $\\ | ||
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* S => aaS => aa | * S => aaS => aa | ||
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