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Let G be the following grammar:

- $S \rightarrow T\dashv $
- $T \rightarrow T aT b \mid T bT a | \epsilon$

- Show that $L(G) = \{w\dashv \: \mid w\: \text{contains equal numbers of a’s and b’s} \}$. Use a proof by induction on the length of $w$.
- Use the DK-test to show that G is a DCFG.
- Describe a DPDA that recognizes L(G).

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