Question: [33] Let x be a binary string. Show that for any positive integer d the number of different descriptions of length C(x) + d of

[33] Let x be a binary string. Show that for any positive integer d the number of different descriptions of length C(x) + d of x is O(2d).

Comments. Source: [G.J. Chaitin, Theoret. Comput. Sci., 2(1976), 45–

48]. See also [R.G. Downey and D.R. Hirschfeldt, Algorithmic Randomness and Complexity, Springer, 2010], Lemma 3.4.2.

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!

Q:

[31] Let x be a binary string of length n, and B1(x, d) be the set of strings y with E1(x, y) d. Let the number of elements in B1(x, d) be denoted by b1(x, d). The set B1 (d, x, n) is defined as...

Q:

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Q:

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...

Q:

DETAILS What is the maximum segment length of a 100Base-FX netdwork, The last character ('X', etc) refers to the line code method used. Line code is a patdtern of voltage, current or photons used to...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

Give Correct ANSWERS Human-Computer Interaction (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages...

Q:

answer all questions promptly What is the maximum segment length of a 100Base-FX netdwork,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current...

Q:

I WILL REJECT AND REPORT THE ANSWER. ANSWER ALL THE QUESTIONS IN DETAILS What is the maximum segment length of a 100Base-FX network, The last character ('X', etc) refers to the line code method used....

Q:

This question involves the use of AGGREGATE linear PYTHOIN regression on the Auto data set. (a) Perform a simple linear regression with mpg as the response and horsepower as the predictor. Describe...

Q:

Prolog You are approached to compose a Prolog program to work with twofold trees. Your code shouldn't depend on any library predicates and you ought to expect that the mediator is running without...

Q:

A transmission case measures W = 0.30 m on a side and receives a power input of Pi = 150 hp from the engine. If the transmission efficiency is = 0.93 and air flow over the case corresponds to T =...

Q:

Agee Company purchased 70% of the outstanding common stock of Himes Corporation. Instructions (a) Explain the relationship between Agee Company and Himes Corporation. (b) How should Agee account for...

Q:

B Accounting 303: Cost Accounting | Official P 16. The operations director does an anal : sis that sh \\ which point the cost per unit jumps shar 5 ows that the cost per unit goes down if they...

Q:

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...