1) Using CYK Algorithm, determine whether the strings aab and abbbb are in the language that is generated by the following grammar:S → AB,       A → BB|a,      B → AB|b 2) For each of the following CFLs L, give a "direct" design of an NPDA (no solutions with CFG pls). i) L1 = {a^n  b^m : 0 ≤ n ≤ m ≤ 3n} ii) L2 = {w ∈ {a, b}* : n_a (w) ≤ 3n_b(w)}      (n_a means n subscript a and n_b means n subscript b)     PLS NO AI GENERATED SOLUTIONS, THANKS A LOT

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.

Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}

NAT Lang processing:  Please explain in detail    Consider a CFG representing a phrase structure grammar for a natural language such as English, including the following rule (the period is part of the rule): S -> NP VP .   In this rule, S, NP, and VP are non-terminal symbols, but we will assume that the period is a terminal symbol specifically representing a period (as opposed to some other end-of-sentence marker). So, we can interpret this rule as stating that a sentence can have the form of a noun phrase followed by a verb phrase followed by a period. (To implement a parser for grammars with rules like this, the tokenizer would have to treat periods as separate tokens.)   Assume that you need to convert this grammar to Chomsky normal form (CNF), perhaps with the CKY parsing algorithm in mind. Using the procedure discussed in class, show the rules that might result from the conversion.

Prove this grammar is Ambiguous <S> -> <A> <A> -> <A> + <A> | <id> <id> -> a | b | c