Chapter 0: Q8P (page 1)

Show that $E Q_{T M}'_{m} E Q_{T M}'$

Short Answer

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Answer:

The proof is given below.

Step by step solution

Turing Machine

A Turing Machine is computational model concept that runs on the unrestricted grammar of Type-zero. It accepts recursive enumerable language. It comprises of an infinite tape length where read and write operation can be perform accordingly.

EQTM 'mEQTM

Let us understand about TM equality. Here,

$E Q_{T M} = {(< M >, < N >) : M, N$ are Turing Machine and language $L (M) = L (N)}$

$E Q_{T M} = {(< M) >, < N >) : M, N$ are Turing Machine and language $L (M) = L (N)}$ ,

Now, $E Q_{T M}'_{M} E Q_{T m} m e a n s t h a t E Q_{T M} i s n o t m a p r e d u c i b l e t o E Q_{T M}$

We will first prove that is not Turing Recognizable.

We know that A' $m B$ : if and only if both A and B are Turing Recognizable or Not-Turing Recognizable.
Now, in our prolem $E Q_{T M_{}}$ , is complement to $E Q_{T M}$ .
Thus, if is $E Q_{T M}$ Turing Recognizable then $E Q_{T M}$ will not be Turing Recognizable and vice versa.

From (1) and (2), we can conclude that is not map reducible to $E Q_{T M}$ , i.e,

$E Q_{T M}'_{M} E Q_{T M}$

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Show that $E Q_{T M}'_{m} E Q_{T M}'$

Short Answer

Step by step solution

Turing Machine

EQTM 'mEQTM

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Show that EQTM'mEQTM'

Short Answer

Step by step solution

Turing Machine

EQTM 'mEQTM

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Game Design in Computer Science

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Study anywhere. Anytime. Across all devices.

Show that $E Q_{T M}'_{m} E Q_{T M}'$