Problem 1. Prove that the following functions are Primitive Recursive.I – 1if x > 0,(1) mPred(x) =for x € N.if x = 0.if x > 0,(2) sgn(x) =for x E N.0 if x = 0.if x > 0,(3) sgn(x) =for x E N.1 if x = 0.

For the above given question the solution is given below:

Problem 1. Prove that the following functions are Primitive Recursive. I – 1 if x > 0, (1) mPred(x) = for r € N. if x = 0. [1 if x > 0, 0if x = 0. (2) sgn(x) = for x E N. %3D if x > 0, (3) sgn(x) = for x Ν. 1 if x = 0.

Problem 1. Prove that the following functions are Primitive Recursive. I – 1 if x > 0, (1) mPred(x) = for r € N. if x = 0. [1 if x > 0, 0if x = 0. (2) sgn(x) = for x E N. %3D if x > 0, (3) sgn(x) = for x Ν. 1 if x = 0.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: Ql: prove using algebraic method that ABC + ĀBC + ABC + ABC = C Q2: Draw the circuit of the…

A: 1.) Algebraic Method

Q: Let f(n) and g(n) be asymptotically nonnegative functions. Using the basic defi- nition of…

A: Your answer is given below.

Q: 5. Find the least integer n such that f(x) is 0(x") for each of these functions 5.a f(x) = 2x² + x³…

Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).

A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…

Q: QUESTION 2 For each pair of functions f(n) and g(n) in the following table, pick 0 if f(n) =…

A: Answer

Q: Show that u is a zero of F(x) if and only if u is a fixed point of f (x) f(x) = x + a F(x). Suppose…

A: For the first part of the problem, A function is given. Now, We can say as a fixed point of if…

Q: A quadratic function is a function of the form f(x) = ax² +bx+c, where a, b, c E R are fixed…

A: Here we have the program defines a function quad_coefficients(f) that takes a function f as input,…

Q: ing lemma to check if the following languages are "regular" or "not regular". Show your complete…

A: Given: L = { w ε {0,1}* :w = 0*(10*)* } Note: A language is regular if and only if it is recognized…

Q: In java and given the following points in a plane(x1,y1) through (x5,y5): (1,3), (2,5), (3,7),…

A: To solve this problem using LPSolve in Java, we first need to define the decision variables,…

Q: We wish to find the length of the longest common sub-sequence (LCS) of X[m] and Yin) as lim.n),…

A: The answer is

Q: Find the Worst case time Complexity of the following recursive function T(n) = T(n-1)+n -1, T(1) = 0…

A: Given:T(n) = T(n-1)+n-1, T(1) = 0Solving it using substitution:T(n) = T(n-1)+n-1 <-(1)T(n-1) =…

Q: Find the relation between the following functions: f(n) = log n and g(n) = Vn. (Square root for…

A: According to our guidelines, we are allowed to solve only the first question. Please post the other…

Q: 6. Suppose functions f(n) > 0 and g(n) > 0 satisfy f(n) = 0(9(n)). Prove or give a counterexample to…

A: Given that, f(n)>0, g(n)>0 and f(n)= O(g(n)) f(n)=n3, g(n)=n3+n, then f(n)= O(g(n)) is true.…

Q: Use a software program or a graphing utility to solve the system of linear equations. (If there is…

A: Since no programming language is mentioned, I am using matlab. Code: syms x1 x2 x3 x4 x5eqn1 = x1 +…

Q: Use the logical programming language PROLOG to solve the following: (reverseo lst result): Logical…

A: In this program we have to execute a prolog program where we have to rotate a list basically reverse…

Q: 3. Use a truth table (either by hand or with a computer program) to prove the commutative laws for ^…

A: The commutative law for ∧ is p∧q≡q∧p lets create truth table for the law p q p∧q q∧p T T T T…

Q: Suppose there is a robot that builds a copy of itself in 2 hours. The copy then starts to build…

A: The solution is given below for the above given question:

Q: Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. 1, Find all the elements of the…

A: Below is the complete answer with explanation in detail for the given question.

Q: Give a recursive definition of the relation is equal to on N x N using the operator s

A: I'm providing the answer to the above question. I hope this will be helpful for you.

Q: x -2x-8 -, X +2 4 a. lim x² -4 X2

A: a. Limits by factoring: Finding a limit by factoring is a technique to finding limits that works by…

Q: Problem 4. Please show the followings: (a) let x and y be real numbers with 0 1 and b > 1.

A: Proved the given functions

Q: Mathematical Induction: Binet's formula is a closed form expression for Fibonacci numbers. Prove…

A: Given the question,

Q: Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point…

A: The fixed point iteration method is method for finding the real root of the non-linear equations by…

Q: Find the Worst case time Complexity of the following recursive functions T(n)=T(n/3)+2T(n/3)+n

Q: 5. Show that for every partially computable function f(x,,..., x,), there is a number m 2 0 such…

A: Answer: I have given answered in the handwritten format

Q: 7. Find a closed form representation for the function defined recursively by f(1) = 10 and…

A: The recursive function is the function in the code which refers itself to the execution. Recursive…

Q: For doing the lab activity: 1) Apply Recursive function technique to solve Problem 1 and 2. (Do not…

A: Since no programming language is mentioned in the question we are doing it in C++ programming…

Q: 5. Prove algebraically, the following: a) (A + B')(A' + B) = AB + A'B' b) AB' + AB + A' = 1 Use only…

A: Given: a) (A+B')(A'+B) = AB + A'B' b) AB' + AB + A' = 1 Requirement: Prove the above two…

Q: Answer the following questions: a) State two advantages of the "orthogonal least square (OLS)'…

Q: Problem 4. Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the…

A: Here is the solution step by step -

Q: g interpolating polynomial

A: This program implements Interpolation Formula in Python Programming Language.In this Python…

Q: Show Let f(.) be a computable, strictly monotonic function, that is, f(n+ 1) > f(n) for all n. Show…

A: If f:Σ∗→Σ∗ is a function, and ∃ a Turing machine which on the input w∈Σ∗ writes f(w), ∀w∈Σ∗, then we…

Q: The function below has the recursive relation T(x,y) = 2T(y/2)+O(1) when x,y>0 Knowing these…

A: According to the question , In part (1) we have to find The worst-case time complexity of the…

Q: What is the time complexity of a program with functions and procedure calls? Given two distinct…

A: A brief explanation of the answer is given below in the image attached below. Please refer to the…

Q: 1. Let f(n) and 8(n) be asymptotically positive functions. Prove or disprove the follow- ing…

A: The solution for the above givenq uestion is given below:

Q: Let f : Z → Z be some function over the integers. Select an appro- priate proof technique (direct,…

A: Answer: I have given answered in the handwritten format in brief explanation

Q: Let set S = {n/n eZ and n is negative), and f be a function defined as f: N S (a) Prove that…

A: The solution to the given question is:

Q: Let S = {3n : neZ}.A recursive definition for the set S is: Basis Step: 3 ES Recursive Step: If a E…

A: I Consider the set S defined recursively as follows:I Base case: 3 ∈ SI Recursive step: If x ∈ S and…

Q: Q10/the minimum sum- of- products for the following function…

A: A'CDE+A'BC'D'E+A'B'C'+A'B'C+A'B'C. Explanation: Approach to solving the question: 1) First, we use…

Question

Problem 1. Prove that the following functions are Primitive Recursive.
I – 1
if x > 0,
(1) mPred(x) =
for x € N.
if x = 0.
if x > 0,
(2) sgn(x) =
for x E N.
0 if x = 0.
if x > 0,
(3) sgn(x) =
for x E N.
1 if x = 0.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Another recursive algorithm is applied to some data A = (a₁, ..., am) where m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is characterised using the following recurrence equations: T(1) = c when the size of A is 1 T(m) = 2T (2) + c otherwise Determine the running time complexity of this algorithm.
A. Show that if p(n) is a polynomial of the form n3 + C2 n? + c1 n + Co, then p(n) = O(n³).
Let the sequence (n) be recursively defined by x1 = √2 and Xn+1 = √√2+xn, n≥ 1. Show that (n) converges and evaluate its limit.
For doing the lab activity: 1) Apply Recursive function technique to solve Problem 1 and 2. (Do not use iterative method) 2) Use map, filter, reduce and lambda functions to solve the problem 3. 1.Evaluate Binomial Coefficient. nCr=n! / (r! *(n-r)!) 2. Fibonacci Numbers (Sequence): 0, 1, 1, 2, 3, 5, 8 …
1(a). For an M/M/1 queuing system, write your own function in R to compute andoutput the:1. long-run probability po,p1,…,pn of there being 0,..,n people in the system.2. the values L, Lq, W, Wq, and Wse. The function should return elements with the names probs (vector of po,…,pn), L, Lq, W,Wq, and Wse (does not have to be in this order) The function should take as inputs, lambda (arrival rate), mu (service rate), and n (thenumber of people to compute probabilities for 0,…,n) Note: you are to code the computations for the above on your own, so none of the functionsin the queueing package are to be used. 1(b). Using your function from 1(a), find the values (b)-(f) in the Queuing Theory(M_M_1).
A recursive algorithm is applied to some data A = (a₁,..., am) where m≥ 2. The running time T is characterised using the following recurrence equations: T(2) = c when the size of A is 2 T(m) = T(m-1) + 2c otherwise Determine the running time complexity of this algorithm.
You are given a third-degree polynomial function f(x) as follows. f(x)=x3-2x2+64x+128 x0=-2.32 (a) Calculate the function value f(x0) and store it in literal (variable) y0. The value for x0 is given in the table.(b) Using Newton's method, find a root for the given function which makes f(x) = 0. The starting point x0 is given in the table. Use error margin as 10−4.Store the root in literal r. Could you write the codes by using Pyhton 3?
11. ) An algorithm X has two parts XA and Xg. In order to complete running algorithm X both parts have to be executed consecutively. If running time of XA is e(f(n)), and running time of Xp is O() then what should be f(n) so that algorithm X has the most efficient solution.
Equation: u_t − (x^2)u_xx = 0 (t, x) ∈ (0,∞) × (0, 5),u(t = 0, x) = 0 for all x,u(t, x = 0) = 100 , u(t, x = 5) = 50. Programing on Matlab solving numerically the problem and Estimate the errors.
Show that if f (n) and g(n) are monotonically increasing functions, then so are the functions f (n) / C g(n) and f g(n) and if f (n) and g(n) are in addition non-negative, then f (n)/g(n) is monotonically increasing.