In each part, find every possible language LC (a, b}* for which the equivalence classes of I are the three given sets. (a, b)* (b}, la, b}*(ba), (A, a} U (a, b}* {aa} (A), (a}({b} U (a}{a}* (b})*. {b}({a} U (b}{b}* {a})*
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- Use the Pumping Lemma to show the following language L is NOT regular. L= {w E (a, b, c}* ; where w has equal number of a's, b's, and c's}A bifunctor is similar to a functor except that it maps two possible types. Define a Bifunctor instance for MkType by defining bimap:: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d . answer in haskell form. thank you.Consider the following language L = {w E {a, b}" : na(w) is not odd}. (a) What class within the Chomsky hierarch does L belong to? (b) Show that L belongs to the class you chose above.
- 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 LemmaProve 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.Show, formally in terms of DFAs, that if L0 is a regular language (has a DFA) and L1 is a regular language (has a DFA), then L0 − L1 must be a regular language as well. Show this by formalizing the difference DFA as we did in class for intersection/union.
- . Prove that the intersection of two context-free languages is not necessarily context-free. This is unlike the case of regular languages which are closed under intersections. Hint: Do something similar to what we did on Activity #21 to show something about two of the languages below and then use what we proved in class about the remaining language. Write several sentences to explain your reasoning. L₁ = {ww has the form a"b"c" for some whole numbers n and m} L2 = {ww has the form amb"c" for some whole numbers n and m} L3 = {w|w has the form a"b"c" for some whole number n}Consider the following language L = {w E {a, b}: Na(w) is not odd}. (a) What class within the Chomsky hierarch does L belong to? (b) Show that L belongs to the class you chose above. Consider the following language L={a*bm c²n+3: n.m>=1}. (a) What class within the Chomsky hierarch does L belong to? (b) Show that L belongs to the class you chose above.For each of the following languages L, state whether or not L is regular. Prove your answer. You can prove it by finding a regular expression that describes the language or by finding an FSM that recognizes it. {w {a, b, c}* : w contains at least two occurrences of the substring ac or w contains no more than 3 c’s}.
- In Haskell lambda expression, (\x -> x * x) (1 + 2) in applicative order. Which is the first, second, third, and fourth redex?Using Haskell or I will give negative on it Write a function which computes the image of R under a (ACST,p.12), where Ris a relation from A to B and a is an element of A based on the representationspecified in (*)The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЄ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.