Question: In Theorem 3.21, we showed that a language is Turing-recognizable iff some enumerator enumerates it. Why didnt we use the following simpler algorithm for the

In Theorem 3.21, we showed that a language is Turing-recognizable iff some enumerator enumerates it. Why didn’t we use the following simpler algorithm for the forward direction of the proof? As before, s₁, s₂, . . . is a list of all strings in Σ^*.

E = “Ignore the input.

1. Repeat the following for i = 1, 2, 3, . . . .

2. RunM on s_i.

3. If it accepts, print out s_i.”

Step by Step Solution

★★★★★

3.32 Rating (164 Votes )

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 Introduction theory computation Questions!

Show that a language is decidable iff some enumerator enumerates the language in the standard string order.

Modify the proof of Theorem 3.16 to obtain Corollary 3.19, showing that a language is decidable iff some nondeterministic Turing machine decides it. (You may assume the following theorem about trees....

In Corollary 4.18, we showed that the set of all languages is uncountable. Use this result to prove that languages exist that are not recognizable by an oracle Turing machine with an oracle for A TM .

Answer the questions numbers 3.1, 3.2, 3.4, 3.5, 3.6, 3.7, 3.8 186 CHAPTER 3 / THE CHURCH-TURING THESIS The following is a high-level description of a TM M that decides A. M = "On input G), the...

3 . 6 In Theorem 3 . 2 1 , we showed that a language is Turing - recognizable iff some enu - merator enumerates it . Why didn't we use the following simpler algorithm for the forward direction of the...

We showed that a language is Turing recognizable iff some enumerator enumerates it. Why didn't we use the following simpler algorithm? Here si, S2, St..is a listing of strings in *. E = "Ignore the...

We showed that a language is Turing recognizable iff some enumerator enumerates it. Why didnt we use the following simpler algorithm? Here s 1 , s 2 , s 3 , is a listing of strings in * . E = Ignore...

Could you please explain to me step by step how to Prove Theorem 3.2.2 by paying attention to proof of Theorem 3.2.1. Theorem 3.2.2: Suppose a = a0 + a1i + a2j + a3k Hs and 2: Hs -> Hs, 2 (a) = 2 (a0...

Let $X_{1}, \ldots, X_{n}$ be a set of independent and identically distributed random variables from a distribution $F$ with variance $\mu_{2}$ where \(E\left(\left|X_{1}ight|^{4}ight) a. Prove...

8.2. (Sec. 8.2) Show that Theorem 3.2.1 is a special case of Theorem 8.2.1. [Hint: Let q = 1, Zo = 1, ~ = JL.)

The pistons of a hydraulic press have radii of 0.543 cm and 3.53 cm, respectively. (a) What force must be applied to the smaller piston to exert a force of 4350 N on the larger? (b) What is the...

Draw up an outline or flowchart tracing the capital budgeting process from the initial idea for a new investment project to the completion of the project and the start of operations. Assume the idea...

Which of the following is an example of a cash equivalent? Customer accounts receivable due within 3 0 days of the balance sheet date Treasury bills with a maturity date of 2 months from the balance...

Which of the following items qualifies for the child care credit claimed by the Rodriguez family? Salary for nanny. Employers share of FICA tax for nanny, paid by Rodriguez. Employees share of...

In Figure 13.14, we illustrate that GTTTAA is a longest common subsequence for the given strings X and Y. However, that answer is not unique. Give another common subsequence of X and Y having length...

What is the longest (proper) prefix of the string "cgtacgttcgtacg" that is also a suffix of this string?

List the prefixes of the string P ="aaabbaaa" that are also suffixes of P.

Consider the following information: State of Probability of State Rate of Return if State Occurs Economy of Economy Stock A Stock B Stock C Boom .66 .09 .03 .24 Bust .34 .13 .19 .04 a. What is the...

I would like for you to briefly review either your personal experiences and/or the financial literature to identify and present a description of one actual capital project/product failure and the...

Problem 4 . ( All cash flows in this problem are in thousands of dollars ) World Airways is considering acquisition of an additional airplane for its short routes. An airplane costs $ 4 0 , 0 0 0 and...