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 $


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.

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  • $\begingroup$ I am confused.. The reason that it doesnt contain any word is that the string production process is infinite, so it cannot product a string ? $\endgroup$ – TuMama Jul 12 at 13:57
  • 1
    $\begingroup$ @TuMama exactly $\endgroup$ – plshelp Jul 13 at 16:04

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