G = ( {A, B}, {a, b}, A, { A → aB, B → aBb, B → λ }), then the string
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Each grammar in Exercises is proposed as generating the set $L$ of strings over $\{a, b\}$ that contain equal numbers of a's and b's. If the grammar generates $L$, prove that it does so. If the grammar does not generate $L$, give a counterexample and prove that your counterexample is correct. In each grammar, $S$ is the starting symbol. $$ S \rightarrow a B|b A| \lambda, B \rightarrow b|b A, A \rightarrow a| a B $$
Automata, Grammars, and Languages
Languages and Grammars
Each grammar in Exercises is proposed as generating the set $L$ of strings over $\{a, b\}$ that contain equal numbers of a's and b's. If the grammar generates $L$, prove that it does so. If the grammar does not generate $L$, give a counterexample and prove that your counterexample is correct. In each grammar, $S$ is the starting symbol. $$ S \rightarrow a S b|b S a| a b S|b a S| S a b|S b a| \lambda $$
Each grammar in Exercises is proposed as generating the set $L$ of strings over $\{a, b\}$ that contain equal numbers of a's and b's. If the grammar generates $L$, prove that it does so. If the grammar does not generate $L$, give a counterexample and prove that your counterexample is correct. In each grammar, $S$ is the starting symbol. $$ S \rightarrow a b S|b a S| a S b|b S a| \lambda $$
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