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https://gateoverflow.in/8159/gate2015-2-35

What are these equations?

$X_0 = 1 X_1$

$X_1 = 0 X_1 + 1 X_2$

$X_2 = 0 X_1 + \{ \lambda \}$

Can we treat them as RIGHT LINEAR GRAMMAR? If yes, then this is the FA for it.Now the question asks for the language of $X_0$ which will be NULL.

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The correct language of $X_0$ can be obtained by REVERSAL of this FA. i.e. by reversing arrows and swapping initial and final states.

I know that when a LEFT LINEAR GRAMMAR is changed to RIGHT LINEAR then language is reversed. But why here?

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