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Let x and y be positive integers, x > 0, y > 0, represented in unary....
Question 2 10 pts Let x and y be positive integers (x, y > 0) represented in unary. Assume that x > y. Design a Turing Machine (TM) that computes the function f (x, y) = 3x – y. More specifically, qow (x) Ow (y) + Ofw (3x – y) 0 Draw the transition graph of the TM, not the block diagram. Make sure you clearly indicate the initial and final states. Here is an example of a computation performed...
02. Design Turing machine to compute the following function for x positive integers represented in unary. f (x) x mod 4.
02. Design Turing machine to compute the following function for x positive integers represented in unary. f (x) x mod 4.
theory of computing
3. Let x be a positive integer represented in unary form. Construct a Turing machine to compute the function fx)-3x (replace the input by function value in unary form (e.g. qo 11 1) Design a grammar for L-(a b cho,n>o).
3. Let x be a positive integer represented in unary form. Construct a Turing machine to compute the function fx)-3x (replace the input by function value in unary form (e.g. qo 11 1) Design a grammar for...
Discrete Mathematical Structures
Draw a Turing machine that takes a string representing two unary numbers, x and y, separated by a 0, and determines whether x greaterthanorequalto y. For example, the input for x = 3, y = 4 would be 11101111. Use two halt states: one for yes and one for no. Give the trace of your machine in the previous problem processing the strings 11101111 and 11110111. Draw a TM that computes f(w) = w^R where w elementof...
Exercise 5. The joint probability density function of X and Y is given by (X,Y)=9) Scy-re-y if y> 0 and -y, y) O otherwise (a) Find c. (b) Find the marginal densities of X and Y. (c) Are X and Y independent?
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
5. Let f(x) = arctan(In x) for all x >0. A graph of y = f(x) is shown in the figure. (a) Find the formula for the derivative f'(x). Then explain how you can deduce from this formula that f is invertible. (b) Find the formula for f-1(x), the inverse of f. (c) What is the domain and range of f-1? (d) Sketch a graph of the function y=f-1(x). (e) Now determine the value of (F-1)(0) using your results from...
3. (a) (5 points) On the set A= R\{0}, let x ~ y if and only if x · y > 0. Is this relation an equivalence relation? Prove your answer. (b) (5 points) Let B = {1, 2, 3, 4, 5} and C = {1,3}. On the set of subsets of B, let D ~ E if and only if DAC = EnC. Is this relation an equivalence relation? Prove your answer.
Let F be the vector field represented in the figure: y X 1Q0Y, 1X P(-1, 1) X Q3.1 3 Points 2d-Curl F(0,0) > 0 O 2d-Curl F(0,0) = 0 2d-Curl F(0,0) < 0 Q3.2 3 Points OV: F(0,0) > 0 OV: F(0,0) = 0 OV: F(0,0) < 0
Below is the p.d.f for the random variables X and Y, f(x,y)-36 0 otherwise Find the following probability Pr(x> 2) O 7/9 2/3 O 8/9