Try this one: Prove that the language L = { 1k1 E N, k-2') is not...
Additional 9-14 Prove that the language {a"b" n, k ε N and n S k} is not regular Hint: I go over this proof in the lecture. You can watch it again to make sure you follow it before doing it. 2 Additional 9-15 Prove that the language (a"b n, k E N and n Hint: a little different... 2 k Is not regular 3 Additional 9-16 Prove that the language (w w (a, b and w has an equal...
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)
Suppose that L is a regular language. Prove that the language p
r e f i x (L )={w |
x, wx
L } is regular. (For example, if L = {abc, def}, prefix(L) = {?,
a, ab, abc, d, de, def}.)
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
Prove that the language L = {0^n1^m0^n | m, n greaterthanorequalto 0} is not regular.
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
Prove that for each regular language L the following language is regular: shift(L) = {uv | vu ∈ L}
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.
Prove that the following language is not regular: L = { w | w ∈ {a,b,c,d,e}* and w = wr}. So L is a palindrome made up of the letters a, b, c, d, and e.