Prove if the following languages are CFL or not. If L is a CFL, give its CFG. Otherwise, prove it by Pumping Lemma. If any closure property of CFL is applicable, apply them to simplify it before its proof. L = {wwRw | w {a, b}*} L = {anbjanbj| n >= 0, j >= 0} L = {anbjajbn| n >= 0, j >= 0}
Problem #4 Consider F = {wi ED" 1 si s 99). Then: (i) Prove that if L is a CFL then in general for all L, L-F is a CFL. (ii) Prove that if L is not a CFL then in general for all L, L-F is not a CFL. (ii) Prove that if L is not a CFL then in general for all L, LUu F is not a CFL. Answer: Problem #4 Consider F = {wi ED" 1...
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)
(20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR WE A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
5. (20 pt.) Prove that the class of regular languages is closed under reverse. That is, show that if A is a regular language, then AR = {wR W E A} is also regular. Hint: given a DFA M = (Q,2,8,90, F) that recognizes A, construct a new NFA N = (Q', 2,8', qo',F') that recognizes AR and justify why your construction is correct.
Is the following language context free or not? (prove / disprove using pumping lemma for CFL ) L = {0n 1 0n | n >= 1}
6.) Is the languages Context Free or not? (prove / disprove using pumping lemma for CFL ) L = {0n 1 0n 10n | n >= 1}
Use the pumping lemma for context-free languages to prove that L3 is not a CFL. L3 = { w: w e{a,b,c}* and na(w) < nh(w) < nc(w) }.
1) Let f:R-->R be defined by f(x) = |x+2|. Prove or Disprove: f is differentiable at -2 f is differentiable at 1 2) Prove the product rule. Hint: Use f(x)g(x)− f(c)g(c) = f(x)g(x)−g(c))+f(x)− f(c))g(c). 3) Prove the quotient rule. Hint: You can do this directly, but it may be easier to find the derivative of 1/x and then use the chain rule and the product rule. 4) For n∈Z, prove that xn is differentiable and find the derivative, unless, of course, n...
Let R be a relation on a set A. Prove that R is antisymmetric if and only if R ∩ R ^(−1) ⊆ {(a, a) : a ∈ A}.