This is a school assignment, I am fairly new to DFA's.

L = {ww|w∈{0,1}*

I feel like I need to put this in words to understand how it works.

Translating L:

W can be a string of an infinite combination of 1s and 0s.
WW is just a string that repeats itself.

For example W="101011", WW = "101011101011".

Im not a 100% on this. Not really sure how to create a DFA out of this.

Am I correct with my "translation"? If you can help me further into making a DFA much appreciated.

  • $\begingroup$ Your language is not regular. $\endgroup$ Feb 1, 2018 at 6:35

1 Answer 1


You cannot make a DFA for this language because its not a Regular language in fact its not even a context free language so you can't even make a PDA for it

to prove its not regular and not context free you should use pumping lemma

but you can make a linear bounded automata for this language so therefore its a context sensitive language

hint for the linear bounded automata: put both of the w's in the tape and separate them with 0, then compare them.

also here's some examples for some of the strings in the language :

00 , 11 , 0101 , 1010 , 110110 ...


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