Question: [35] Show that there is a computably enumerable set A with characteristic sequence such that for all total computable functions t, and for all

[35] Show that there is a computably enumerable set A with characteristic sequence χ such that for all total computable functions t, and for all 0

cn.

Comments. Compare this exercise with Theorem 7.1.3.

R.P. Daley [Inform. Contr., 23(1973), 301–312] proved a more general form of this result using the uniform complexity of Exercise 2.3.2, page 130.

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:

[23] Assume the terminology in Exercise 6.8.7. Consider defined in the proof for Item (ii) of Barzdinss lemma, Theorem 2.7.2. Essentially, i = 1 if the ith bit of U(i)

Q:

[35] We have characterized the regular languages using Kolmogorov complexity. It is immediately obvious how to characterize computable languages in terms of Kolmogorov complexity. If L and = {v1,...

Q:

[27] Is there a symmetric form of Theorem 2.7.2 (Barzdinss lemma) using only conditional complexities? The answer is negative. Show that there is no computably enumerable set such that its...

Q:

[39] We assume familiarity with the notion of truth-table reducibility. Let be the characteristic sequence of a computably enumerable set A. Here C(1:n; n) is the uniform complexity of Exercise...

Q:

[35] Show that there exists an infinite binary sequence which is not random in the sense of Martin-Lof with respect to any computable measure. Comments. Source: [A.K. Zvonkin and L.A. Levin, Russ....

Q:

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

Q:

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

Q:

an operation that yields a N aN value when neither of its arguments is a N aN, (b) an operation with finite arguments that yields +, (c) an operation with an argument + that yields a finite result....

Q:

[35] Use the definitions given earlier. The following is known as Posts problem (1944). The computable sets have lower r-degree of unsolvability than K0, which has the highest r-degree of...

Q:

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

Q:

Fifth Season Community Bank has identified that it holds $212 million in rate-sensitive assets and $309 million in rate-sensitive liabilities. What is the bank's expected change in net interest...

Q:

What do the ideas of Rousseau, Darwin, and Hall have in common?

Q:

5 6 minutes remaining 2 2 OF 2 5 QUESTIONS REMAINING Which one of the following statements related to risk is correct? None of these are correct Portfolio beta can be effectively lowered by adding T...

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...