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--- lfa:lab09-cfl [2021/11/30 10:52]
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+++ lfa:lab09-cfl [2021/11/30 11:05] (current)
pdmatei
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-====== L09. Context-Free Languages ======
+====== 9. Context-Free Languages ======
+===== 9.1. Accepting and generating a CF language =====
+Write a PDA as well as a CF grammar for the following languages. Specify - for each PDA, the way it accepts (by empty-stack or by final state). For each grammar, make sure it is not ambiguous. (Start with any CF grammar that accepts L. Then write another non-ambiguous grammar for the same language).
+**9.1.1.** $ L = \{\: w \in \{A,B\}^* \ | \:w \text{ is a palindrome}\} $.
+**9.1.2.** $ L = \{ A^{m} B^{m+n} C^{n} \ | \: n, m \geq 0 \} $
+**9.1.3.** $ L = \{w \in \{a, b\}^* | \#_a(w) = \#_b(w) \} $
+**9.1.4.** $ L = \{w \in \{a, b\}^* | \#_a(w) \neq \#_b(w) \} $
+**9.1.5.** $ L = \{a^ib^jc^k | i = j \lor j = k \} $ \\
+===== 9.2. Ambiguous grammars =====
+Which of the following grammars are ambiguous? Justify each answer. Modify the grammar to remove ambiguity, wherever the case.
+**9.2.1.**
+$ S \leftarrow aA | A $ \\
+$ A \leftarrow aA | B $ \\
+$ B \leftarrow bB | \epsilon $
+**9.2.2.**
+$ S \leftarrow AS | \epsilon $ \\
+$ A \leftarrow 0A1 | 01 | B $\\
+$ B \leftarrow B1 | \epsilon $
+**9.2.3.**
+$ S \leftarrow ASB | BSA | \epsilon $\\
+$ A \leftarrow aA | \epsilon $\\
+$ B \leftarrow bB | \epsilon $
+**9.2.4.** Write an ambiguous grammar for $ L(a^*) $.