Given the language L = {(01)n| n > 1000000}. State whether it is a regular language or non-regular language. Prove your statement.
Given the language L = {(01)n| n > 1000000}. State whether it is a regular language...
Prove that for each regular language L the following language is regular: shift(L) = {uv | vu ∈ L}
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 the language L = {0^n1^m0^n | m, n greaterthanorequalto 0} is not regular.
3. [5 marks] Is the language L = {o € {a, b}* | |0la- l0b is divisible by 2",n 2 1} regular? Be sure to prove your answer
3. [5 marks] Is the language L = {o € {a, b}* | |0la- l0b is divisible by 2",n 2 1} regular? Be sure to prove your answer
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.
Let L be the language {0n 1m : n ≤ m ≤ 2n}. Is L regular? contextfree but not regular? or not context-free? Show that your answer is correct.
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
Consider the language L below. (a) Is L a regular language? –
Yes, or No. (b) If L is a regular language, design the DFA (using a
State Table) to accept the language L, with the minimum number of
states. Assume , (c) Suppose the
input is “101100”. Is this input string in the language L?
Σ = {0,1} L={w l w has both an even number of O's and an odd number of 1's}
[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