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Is the language $L =$ {$a^nb^n : n ≥ 1$} $∪$ {$b$} deterministic?

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$L_1$=$\{a^nb^n:n\ge 1\}$ is DCFL

$L_2$=$\{b\}$ is Regular

&, DCFL $\cup$ Regular = DCFL.

thus, $L=\{a^nb^n:n \ge 1\} \cup \{b\}$ is DCFL.

Hence, deterministic.

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