Using Python programming language. There are exactly N people living in a certain parallel universe. The Ith of these N people claim to be the parent of exactly Ai off these N people. However, some of these people may be lying - the person may either be telling the truth (in which case they have exactly Ai children) or lying down (in which case they can have any number of children). It is known that each person has at most one parent. Furthermore, as one would expect, a person's child is not allowed to also be their ancestor. What is the maximum possible number of truth tellers in this universe Possible input Required Output 1 2 2 10

Suppose you have a computer that requires 1 minute to solve problem instance of size 210. What instance sizes can be run in 1 minute on a computer 256 times faster than the first one assuming the following complexities?   (a) Θ (n2 )   (b) Θ (logn)    (c) Θ ( 2n )   (d) Θ (SquareRoot(n))

Suppose we have four machines that are using the Berkeley algorithm for clock synchronization. The time daemon is running on machine MO. The other machines are named M1, M2, and M3. The time readings on the four machines are as follows wenty-four hour clocks are usedt. MO 09:10 M1: 08:30 M2 10:10 M3: 07:14 In the third step of the algorithm, what are the values that the time daemon sends to each machine? Assume that the time values are expressed in minutes. Below, these values are presented in a vector value sent to MO, value sent to MI, value sent to M2. value sent to M3I none of these O84, 44, 96, 321 O(24, 16, -84, 92) O192. 84, 16. -24 O-32, 76, 40

The extraterrestrials living in the planet Numerion revere a specific type of integers N. In particular, for those creatures, an integer N is holy if there exists an integer i >= 1 such that:N = i*i + iHere are some examples of holy numbers:2 (because 2 = 1*1 + 1) 6 (because 6 = 2*2 + 2) 12 (because 12 = 3*3 + 3) In a file called Numerion.java, write a program that: Asks the user to enter an integer N. It is OK if your program crashes when the user does not enter a valid integer. Prints out whether that number is a holy number in planet Numerion. For example: if the user enters 25, your program output should look EXACTLY like this: Enter an integer N: 25 25 is not a holy number in Numerion. Exiting... As another example: if the user enters 12 (a holy number, since 12 = 3*3 + 3), your program output should look EXACTLY like this:Enter an integer N: 12 12 is a holy number in Numerion. Exiting...

A 2-dimensional Turing machine has an infinite 2-dimensional grid asits storage device (one cell for every address (i, j) ∈Z×Z). Instead ofL and R, there are 5 options for the head to move from (i, j): Left (to(i −1, j), Right (to (i + 1, j)), Up (to (i, j + 1)), Down (to (i, j −1)),and Stay (remain at (i, j)) .Let us assume, that our 2-dimensional TM M has an additional 1-dimensional tape where the input is located as in a 1-tape TM. The2-dimensional storage device contains a blank symbol in every cell atthe start of the computation.Show that a 2-dimensional TM is not more powerful, i.e., every lan-guage accepted by a 2-dimensional TM M is accepted by one of ourstandard 1-dimensional TMs. You don’t have to simulate directly witha 1-tape TM, as you are allowed to use what we know about k-tape(1-dimensional) TMs without proof.Describe the moves of a simulating TM M ′ in plain English. For everypossible move of M , you have to design a sequence of moves of M ′that simulates that move of…

In Fibonacci's model, rabbits live forever. The following modification of Definition 3.1 accounts for if n ≤ 0 if n = 1 or n = 2 G(n) = 1 (a) Compute G(n) for n = 1, 2, ..., 12. G(1) G(2) G(3) G(4) G(5) G(6) G(7) G(8) G(9) G(10) G(11) G(12) = = = = = = = = G(n-1) + G(n − 2) - G(n - 8) if n > 2. - = (b) In this modified model, how long do rabbits live? months

Consider the Turing Machine defined as follows: (q0,0,q0,0,R), (q0,1,q1,0,R), (q0,B,q2,B,R), (q1,0,q1,0,R), (q1,1,q0,1,R) and (q1,B,q2,B,R). Describe what this TM does when presented with bit strings defined over the alphabet Σ = {0,1} as input. (Note: B = Blank).