Find a context-free grammar for each of the following languages over the alphabet {a, b}. (N: the natural number set) a. {anb2n | n ∈ N U {0}} U {an+2bn | n ∈ N} b. {ambn | m, n ∈ N, and n > m}.

Prove that the following language is regular.L = {x | x ∈ {0, 1}∗, x does not contain five consecutive 0's or five consecutive 1's}Hint: You may take advantage of some closure properties.

Write a complete CFG that recognizes the language: L = {aibj | i ≤ j}

Q: Let Ls= {|R1 and R2 are regular expressions and L(R1) = L(R2)}. Ls is a language containing all strings that contain pairs of regular expressions that accept the same language. Show that Ls is decidable.

L = {am+n bm cn | m,n ≥ 1} over Σ = {a, b, c}   A. Design PDA for L (with as less as states possible) B. Is L is regular language? C. Verify it by Pumping Lemma

Q6: Give context-free grammars that generate the following languages: w = 10 {w€ {0, 1}* ||w| is even }, |w| means the size of the string {w € {0, 1}* | the length of w is odd and the middle symbol is 0} ●

Let { a b } be the alphabet set. Write a Context free grammar CFG for each of the followinglanguages:a) L = Language of all palindromeb) L = language of equal no of a’s and b’c) { \ m ≠ n, m, n ∈ N}d) R.E. = b(a+b)*e) R.E. = (ab + b)*f) R.E. = ab(ba)* + bb please solve all the parts kindly