Use the pumping lemma to prove the following language is nonregular:L = {anb3n} = {abbb, aabbbbbb, aaabbbbbbbbb, …}
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Use the pumping lemma to prove the following language is nonregular:
L = {anb3n} = {abbb, aabbbbbb, aaabbbbbbbbb, …}
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- Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈ {a,b}* ∧ w is a substring of t}Find closed form representation for recursively defined function: T(n) = 7, when n = 1 T(n) = 5T(n/4) + n^2, when n > 1. Explore power of two. Find closed form representation in the form where T(n) = A*n^B + C*n^D. Find A, B, C, and D. Hint: T(4) = ?, T(4^2) = ?, T(4^3) = ? to find the patten.For the following pairs of expressions, find a unifier for each pair if a unifier exists. If a unifierdoes not exist, explain why.(a) p(X,Y) and p(a,Z)(b) p(X,X) and p(a,b)(c) f(X,Y) and f(a,g(a))(d) q(X) and ¬q(a)
- A set of expressions is unifiable if and only if there exists only one (unifying) substitution that make the expressions identical.i-Trueii-Falsewith explanUsing the following variable bindings: (setq x ‘(a b c d)) (setq y ‘(1 2 3 4)) Using only variables x and y, car, cdr, and cons, provide Lisp S-expression to generate: (a 1) (b 2) (c 3) (d 4))
- Find a most general unifier (if one exists) of the following pairs. P(y,a,b,y) and P(c,f,g,f) where a and b are constants, and f,g,y are variables. P(f(x),r(x),c) and P(w,r(q),q), where c is a constant, and x, w, q are variables.PLEASE MAKE IT NEAT AND STATE ANY LEMMAS USEDEven if CNF may be converted to DNF, why is it easier to satisfy Disjunctive Normal Form (DNF) than Conjunctive Normal Form (CNF) in run time?
- Computer Science For the following lambda calculus term, reduce it to a normal form. Be careful with parentheses and show every beta-reduction step. (lambda n. lambda m. lambda f. lambda x. m f (n f x)) (lambda f. lambda x. f x) (lambda f. lambda x. f (f x))Describe the following sets by regular expressions, (a) {abba} (b) {a, ab} .In the WHILE language, prove that if <while b do y := y-x,s> ⇓ s' then there exists an integer k such that s(y) = s'(y) + k * s(x) Please use induction on derivations, with induction hypothesis.