Let p be the pumping length.
Let S = (0^p)(1^p)(0^p)
Breaking this into xyz.
As |xy|<=p and |y|>0 so y = 0^k for k>0
So x(y^2)z = (0^(p+k))(1^p)(0^p)
Prove that the language L = {0^n1^m0^n | m, n greaterthanorequalto 0} is not regular.
Prove that the following are not regular languages. Just B and F please Prove that the following are not regular languages. {0^n1^n | n Greaterthanorequalto 1}. This language, consisting of a string of 0's followed by an equal-length string of l's, is the language L_01 we considered informally at the beginning of the section. Here, you should apply the pumping lemma in the proof. The set of strings of balanced parentheses. These are the strings of characters "(" and ")"...
construct a context free grammar for the language l {a^nc^mb^n: n,m Greaterthanorequalto 0}
Prove that the language is regular or not. {a^nb^m | n >= m and m <= 481}
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
Prove that for each regular language L the following language is regular: shift(L) = {uv | vu ∈ L}
Prove that the following language is regular or explain why it is nonregular: L = {amb" (m is odd and n is even) OR (m is even and n is odd))
Find a minimal DFA for the following language. And Prove that your result is minimal. L = {a^n: n greaterthanorequalto 0, n notequalto 2}.
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
Prove that language L on {a, b}, L={ v | v = vR} is not regular 4. (20 points) Prove that language Lon{a, b}, L={v | V = VR} is not regular.
[10 marks] We know from our discussion that the language Onlnln-0} is not regular. Is the language L {0"w1nIn 〉 0, w E {0, 1)'} regular! Be sure to prove your answer [10 marks] We know from our discussion that the language Onlnln-0} is not regular. Is the language L {0"w1nIn 〉 0, w E {0, 1)'} regular! Be sure to prove your answer