Question: [25] Prove that for each binary string x of length n there is a y equal to x except for one bit such that C(y|n)

[25] Prove that for each binary string x of length n there is a y equal to x except for one bit such that C(y|n) ≤ n − log n + O(1).

Comments. Hint: The set of binary strings of length n constituting a Hamming code has 2n/n elements and is computable. Source: personal communication, I. Csisz´ar, May 8, 1993.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Elementary Probability For Applications Questions!

[23] Let 1, 2,... be the effective enumeration of partial computable functions in Section 1.7. Define the uniform complexity of a finite string x of length n with respect to (occurring in the above...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Priority reversal can happen when strings of varying needs synchronize on admittance to normal assets - strings of more prominent need might wind up looking out for strings of lesser need, prompting...

MAT348-Homework # 3 (20 points, due on Wednesday March 23) Question 1. Let S1 ((Z 26 )10 , (Z 26 )10 , (Z 26 )* , e (1) , d (1) ) be the multiplicative cipher defined by e(1) ( x0 ,, x9 ) (k1 x0 mod...

answer this question as soon as possible. the worksheet 8 is given below all the last three files are given below. the first file is 1000 prime text it contain text 1 from 7919 numbers. second file...

/// file some fun help(the code is bellow) #include #include #include #include #include using namespace std; constexpr int N = 8; // number of bits typedef enum BIT{ zero = 0, one = 1 }; // bit //...

4. Consider the following variant of string alignment: given two strings x, y, and a positive integer L, find all contiguous substrings of length at least L that are aligned (using no-ops...

One's Complement one to one 2. The one's complement representation of an integer is denned as follows: 0(x)2 ifx>0. (2" - 1)2 ecall that ()2 denotes plain binary representation, and 0 as a prefix...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Discuss why is cultural relativism important for Americans?

The Maricopa Foundation for Medical Care was a nonprofit organization established by the Maricopa County Medical Society to promote fee-for-service medicine. Roughly 70 percent of the physicians in...

Meghna is the sole shareholder and CEO of BQT . BQT is a very profitable S corporation. Until recently, Meghna's salary was in line with the salaries of comparable CEOs. However, Meghna recently...

a. Financial statements should aid the user of the statements in making decisions. In your opinion, would the user of the statements be aided if there were a distinction between financial reporting...