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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...
[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
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 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 language L = {0^n1^m0^n | m, n greaterthanorequalto 0} is not regular.
Prove that language L on {a, b}, L={ v | v = vR} is not regular use string ab^nab^na
Prove that language Lon {a, b}, L={ vv = v*} is not regular.
Prove that language Lon{a,b}, L={ vv = vR} is not regular.
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
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}*}
Let Σ = { a } , and consider the language L = { a n : n is a prime number } = { a 2 , a 3 , a 5 , a 7 , a 11 , . . . } . Is L a regular language? Why or why not? (Hint: L contains a 11 , a 17 , a 23 , a 29 , but not a 77 since 77 is divisible by 11. ....