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[jayaswalsnehil]

Please tell me the explanation and answer of following questions:

1. how many 2 state Finite automata can be drawn which accepts empty language?

2. fsm with output capability can be used to add two integers in binary representation?

3. sum of regular language and Non-regular language is regular?


4. String of 0's whose length is a perfect square is regular language?

5. If R is regular and N is non-regular ,then R+N is regular?

[jayaswalsnehil]

please answer my previous question of TOC, please

[BhaskarMukhoty]

I will answer the last one first, and this should cover the third one also, as "sum of language" should mean union of language.

Ans to 3 and 5:

Regular languages are closed under union, intersection and complementation set operations.

Since A - B = A intersection (complement of B), regular languages are closed under set substraction operation too.


Now consider R+N to be regular.

then, So is (R+N)-R

Which implies N is regular, a contradiction.

Hence, R+N is not regular.

[BhaskarMukhoty]

Ans to 4:


String of 0's whose length is perfect square, could not be regular.
This can be proved using pumping lemma for regular languages.