*This question was made during a class of Computer Theory in Rome, Italy.*

Let $G$ be a regular grammar, $\Sigma$ its alphabet and $L(G)$ the language generated by $G$

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> Given a regular grammar $G$, is $L(G) = \Sigma^\*$ a decidable property? 
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**My approach**

I can design a Finite State Automaton that recognize the strings in the language $G$. Because regular languages are closed under the iteration operation, the FSA recognize also string in $\Sigma^\*$ alphabet