This was a homework-related assignment trouble which I understand I have actually incorrectly answered. I gave:

S -> ""meaning that S returns the empty string. I understand that the empty collection and empty string are not the very same. According to my professor, the answer is:

S -> SNow, that answer appears strange to me:

It will certainly never before terminate.It isn"t so a lot a language as the absence of one.

You are watching: Is the empty set a regular language

I understand also from a strictly mathematical standsuggest, I"m not going to acquire all over through number 2. However before, is it compelled for a language to terminate? Having a language that CAN go on forever sounds okay, but one that never before will certainly terminate sounds wrong enough that I assumed I"d ask if anyone knows if that"s a language necessity or not.


From the Formal Grammar Wikipedia page:

the language of G, denoted as L(G), is characterized as all those sentences that deserve to be obtained in a finite number of actions from the begin symbol S.

Starting through S, applying the production ascendancy when to S provides S. Applying the preeminence twice provides S. By induction, applying the dominance any type of finite number still gives S. Because no sentences deserve to be acquired in a finite number of steps, the language is empty, so your professor is correct.

Alternative means to specify a grammar that accepts the empty set are L(G) = (the language is empty) or P = (the collection of production rules is empty).


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