Q14P Prove that ifNEXPTIME鈮燛XPTIME,... [FREE SOLUTION]

91影视

Introduction to Theory of Computation

Michael Sipser

Computer Science

3rd Edition 路 458 pages

ISBN: 9781133187790

Chapter 9: Q14P (page 390)

Prove that if $NEXPTIME 鈮� EXPTIME$ , then $P 鈮� NP$ . You may find the function pad, defined in problem 9.13, to be helpful.

Short Answer

Expert verified

If $NEXPTIME 鈮� EXPTIME$ , then $P 鈮� NP$ proved by taking its contrapositive i.e., If $P = NP$ then $NEXPTIME 鈮� EXPTIME$ ,

Step by step solution

Assuming and proving the contrapositive

If $L 鈭� NTIME (2^{2^{掳}})$ then the language $L_{pad} = {< x, 1^{2 |x| 掳} > : x 鈭� L}$ is in NP. This process of adding a string of symbols to each string in the language is known as padding.

So, if $P = NP$ then $L_{pad}$ is in P but if $L_{pad}$ is in P then L is in EXPTIME.

Using the polynomial-time machine

In order to conclude whether an input x is in L, it just pads the input and decides whether it is in $L_{pad}$ (Using polynomial-time machine for)

Hence, we can say that if $P = NP$ is assumed then NEXPTIME =EXPTIME and so it can also be said that if $NEXPTIME 鈮� EXPTIME$ , then $P 鈮� NP$ .

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91影视

Prove that if $NEXPTIME 鈮� EXPTIME$ , then $P 鈮� NP$ . You may find the function pad, defined in problem 9.13, to be helpful.

Short Answer

Step by step solution

Assuming and proving the contrapositive

Using the polynomial-time machine

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91影视

Prove that ifNEXPTIME鈮�EXPTIME, then P鈮�NP. You may find the function pad, defined in problem 9.13, to be helpful.

Short Answer

Step by step solution

Assuming and proving the contrapositive

Using the polynomial-time machine

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Issues in Computer Science

Game Design in Computer Science

Data Structures

Computer Network

Cloud Services

Study anywhere. Anytime. Across all devices.

Prove that if $NEXPTIME 鈮� EXPTIME$ , then $P 鈮� NP$ . You may find the function pad, defined in problem 9.13, to be helpful.