#### Question Details

[solution]: NOTE: Each problem set counts 15% of your mark, and it is

Answer download

More Details:

NOTE: Each problem set counts 15% of your mark, and it is important to do your own

work. You may consult with others concerning the general approach for solving problems on

assignments, but you must write up all solutions entirely on your own. Copying assignments

is a serious academic offense and will be dealt with accordingly.

1. The decision problem PARTITION is defined on page 13 of the Notes NP and NPCompleteness". (You may assume that a1; : : : am are positive integers.)

Define the associated search problem PARTITION-SEARCH and give an algorithm

showing that

PARTITION-SEARCH ! p PARTITION.

Give a loop invariant for your algorithm.

(See Definition 6 in the Notes Search and Optimization Problems" for the definition

of ! p .)

2. Consider the problem DISTANCE-PATH.

DISTANCE-PATH

Instance

hG; s; t; di, where G is an undirected graph, s and t are nodes in G, and d is a positive

integer.

Question Is the distance from s to t exactly d? In other words, is it the case that there

is a path of length d from s to t, and no shorter path from s to t?

(a) Show that DISTANCE-PATH 2 NL.

(b) Show that DISTANCE-PATH is NL-complete.

Hint: Show that P AT H ?L DISTANCE-PATH. Given a directed graph G construct

an undirected graph G0 by making n copies of G. Each edge in G0 goes from copy i to

copy i + 1.

3. Use a padding argument to show that NL = coNL implies NSPACE(n3) = coNSPACE(n3).

See Problem 9.13, in the textbook for a description of padding.

4. Show that T QBF = 2 DSPACE(n1=5). You may refer to the proof of Theorem 8.9 in

the text, and assume the fact that the reduction presented there can be carried out in

log space.

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Dec 18, 2020 *

* * Solution~00031148133888.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free copy (Deadline assured. Flexible pricing. TurnItIn Report provided)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDDec 18, 2020

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN YOUR SET DEADLINE.