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Are there languages generated by linear grammer which aren't regular?

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up vote 4 down vote accepted

Of course. Look at the first example on Wikipedia:

$\qquad S \to aSb \mid \varepsilon$

is linear and generates $\{a^nb^n \mid n \in \mathbb{N}\}$, a non-regular language.

If you mean left-linear, or right-linear, then no - they are equivalent to REG.

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