CFG-Infinite recursion

Question

As you see, the string production process never ends.

Can someone explain me if this language is regular or not ?

$ S \to Α Β S $

$ A \to S $

$ B \to a B b $

Answer 1

The language is regular: $$ L = \{\}$$ It doesn't contain any word not even the empty word $\varepsilon$. The automaton recognizing it has only one state; a reject state. Or if you are using DFA the automaton just wouldn't have an accept state.

Notice that the language is regular but that the grammar is written in a form that's usually used for context free grammars, but the language produced by it is still regular.