Apply master theorem and find the time efficiency of i) T(n) = 2T(n/2)+nlogn
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Q: Calculate time complexity using amortized analysis
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Apply master theorem and find the time efficiency of i) T(n) = 2T(n/2)+nlogn ii) T(n) = (2^n)T(n/2)+(n^n) |
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- AES uses operations performed over the finite field GF(2^8) with the irreducible polynomialx8 + x4 + x3 + x + 1. Q: In a finite field GF(2^8) with the irreducible polynomial x^8 + x^4 + x^3 + x + 1, given two bytes of inputs, explain how the addition works.Theory of Computation Prove that XY is undecidable XY = { ⟨M⟩ ∣ M is a TM where x∈L(M) and y∈L(M) } Prove this by reducing it from ATM which is proven to be undecidableConsider a telegraph source having two symbols, dot and dash. The dot duration is 0.2 second. The dash duration is three times the dot duration. The probability of the dot’s occurring is twice that of the dash, and the time between symbols is 0.2 second. Assume n = 2 ( 2nd extension of the code), pdash = S0 and pdot = S11. Determine the equivalent codeword for each symbol using Shannon Code. Supersymbol Code S0 S0 S0 S1 S1 S0 S1 S1 2. Determine the coding efficiency.
- evaluate nCxpxqn-x for the values of n, x, and p given in Problem A) n= 4, x= 2, p=1/2Suppose N is an RSA modulus, and x^2 ≡N y^2, but x≡N ±y. Show how to efficiently factorN when such a pair x and y are known. ************* WRITTEN AS A SAGE FUNTION*****************Show that ∃x (P (x) ∧ Q(x)) is not logically equivalent to (∃x P (x)) ∧ (∃x Q(x)).
- Find its time complexity using Big-O Notation.Use functional decomposition for the function f(x1 x2 x3 x4 x5) = Σm(1, 2, 7, 9, 10, 18, 19, 25, 31) + D(0, 15, 20, 26). how does your implementation compare with the lowest-cost SOP implementation? Give the costs. Mostly confused on how to use functional decomposition in general.(a) Given a DFA M = (Q, Σ, δ, q0, F), consider M' = (Q, Σ, δ, q0, F'), where F' = Q − F. Prove that L(M') is the complement of L(M). (b) Give a counter-example to show that the above construction with NFAs does not (always) yield the complement.
- Calculate time complexity using amortized analysisLet an optimal prefix-free code be S if x and y are characters with frequencies f(x) and f(y) such that f(x)<f(y), then prove that b(x)>=b(y) [here "b" represents the number of bits that S uses to encode a character]log n, nn, n!+n, 10 root n, n4+n3, 22n, 3n, 500n+root n Arrange functions in increasing order of complexity.