answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
uysha [10]
2 years ago
4

In the EXACT 4SAT problem, the input is a set of clauses, each of which is a disjunction of exactly four literals, and such that

each variable occurs at most once in each clause. The goal is to nd a satisfying assignment, if one exists. Prove that EXACT 4SAT is NP-complete.
Computers and Technology
2 answers:
lord [1]2 years ago
7 0

Answer:

Explanation:

To prove that EXACT 4-SAT is NP-complete, we prove that 4-SAT is in NP and NP-hard.

Firstly, 4-SAT is in NP, we can denote a nondeterministic polynomial-time algorithm which will take a 4-SAT instance and for input it takes a proposed truth assignment. This algorithm assess the 4-SAT instance with the truth assignment. If the 4-SAT instance assess to true, the algorithm gives the output yes; else, the output is no. This runs in polynomial time. To prove that 4-SAT is NP-hard, we reduce 3-SAT to 4-SAT as follows.

Let ? denote an instance of 3-SAT. We convert ? to a 4-SAT instance ? ? by turning each clause

(x ? y ? z) in ? to (x ? y ? z ? h) ? (x ? y ? z ? ¬h),

where h is a new variable. Clearly this is polynomial-time doable.

? If a provided clause (x ? y ? z) is contented by a truth assignment, then (x ? y ? z ? h) ? (x ? y ? z ? ¬h) is contented by the similar truth assignment with h arbitrarily set. Thus if ? is contentable, ? ? is contentable.

? Imagine ? ? is contented by a truth assignment T. Then (x ? y ? z ? h) ? (x ? y ? z ? ¬h) must be true under T. As h and ¬h assume different truth values, x?y?z must be true under T as well. Thus ? is contentable.

Nuetrik [128]2 years ago
6 0

Answer:

To prove that 4-SAT is NP-complete, we need to prove that 4-SAT is in NP and NP-hard both.

Case 1:

We can write a non-deterministic algorithm that will take an instance of 4-SAT and a truth assignment. Then it would verify if the instance evaluates to true.

This algorithm will take polynomial time. So 4-SAT is in NP.

Case 2:

Now let us reduce 3-SAT to 4-SAT, to prove 4-SAT in NP-hard.

Let say we have a 3-SAT instance C, where each clause is consisting of three literals.

Now to find the equivalent 4-SAT C’, replace each clause (p ∨ q ∨ r ) as (p ∨ q ∨ r ∨ s) ∧ (p ∨ q ∨ r ∨  ¬s).

• If the 3-SAT C is satisfiable by a truth assignment, then also C’ is satisfiable. As if we have the truth assignment for (p ∨ q ∨ r ), then we can find the same for (p ∨ q ∨ r ∨ s) ∧ (p ∨ q ∨ r ∨  ¬s).

• And if there is some truth assignment for C’, then that C will be satisfiable under the same assignment. Because if (p ∨ q ∨ r ∨ s) ∧ (p ∨ q ∨ r ∨  ¬s) is true then (p ∨ q ∨ r ) can be true.

Hence 4-SAT is in NP-hard.  

Due to both cases, 4-SAT is NP-complete.

You might be interested in
Juan, a network user, sends an email to you, the IT admin of the network, stating that his account is locked because he has lost
slamgirl [31]

Answer:

The correct answer to the following question is Option D.

Explanation:

Already when we authorize an individual to set up a new credential or provide a provisional code or password, we must make ensure that the person is checked. We could allow a verification code after confirming the consumer.

  • Verification remains crucial because an imposter may try to compromise to provide a temporary credential or switch his password by posing as a further person.
  • So, Juan fixes his problem by making sure whether resetting the password has always been allowed by checking that Juan is the one that he claims he is.

8 0
2 years ago
15. It is the process of capturing data or translating information to recording format
Helen [10]

Answer:

A Documentation, hope this helps.

5 0
2 years ago
Robin wants her presentation to move from one slide to another with special motion effects. Which option should Robin use?
topjm [15]
If this is in power point, then she should use the <em>transitions </em>tab on the ribbon. =)
3 0
2 years ago
Read 2 more answers
Modify the TimeSpan class from Chapter 8 to include a compareTo method that compares time spans by their length. A time span tha
My name is Ann [436]

Answer:

Check the explanation

Explanation:

Here is the modified code for

TimeSpan.java and TimeSpanClient.java.

// TimeSpan.java

//implemented Comparable interface, which has the compareTo method

//and can be used to sort a list or array of TimeSpan objects without

//using a Comparator

public class TimeSpan implements Comparable<TimeSpan> {

   private int totalMinutes;

   // Constructs a time span with the given interval.

   // pre: hours >= 0 && minutes >= 0

   public TimeSpan(int hours, int minutes) {

        totalMinutes = 0;

        add(hours, minutes);

   }

   // Adds the given interval to this time span.

   // pre: hours >= 0 && minutes >= 0

   public void add(int hours, int minutes) {

        totalMinutes += 60 * hours + minutes;

   }

   // Returns a String for this time span such as "6h15m".

   public String toString() {

        return (totalMinutes / 60) + "h" + (totalMinutes % 60) + "m";

   }

   // method to compare this time span with other

   // returns a negative value if this time span is shorter than other

   // returns 0 if both have same duration

   // returns a positive value if this time span is longer than other

   public int compareTo(TimeSpan other) {

        if (this.totalMinutes < other.totalMinutes) {

            return -1; // this < other

        } else if (this.totalMinutes > other.totalMinutes) {

            return 1; // this > other

        } else {

            return 0; // this = other

        }

   }

}

// TimeSpanClient.java

public class TimeSpanClient {

   public static void main(String[] args) {

        int h1 = 13, m1 = 30;

        TimeSpan t1 = new TimeSpan(h1, m1);

        System.out.println("New object t1: " + t1);

        h1 = 3;

        m1 = 40;

        System.out.println("Adding " + h1 + " hours, " + m1 + " minutes to t1");

        t1.add(h1, m1);

        System.out.println("New t1 state: " + t1);

        // creating another TimeSpan object, testing compareTo method using the

        // two objects

        TimeSpan t2 = new TimeSpan(10, 20);

        System.out.println("New object t2: " + t2);

        System.out.println("t1.compareTo(t2): " + t1.compareTo(t2));

        System.out.println("t2.compareTo(t1): " + t2.compareTo(t1));

        System.out.println("t1.compareTo(t1): " + t1.compareTo(t1));

   }

}

/*OUTPUT*/

New object t1: 13h30m

Adding 3 hours, 40 minutes to t1

New t1 state: 17h10m

New object t2: 10h20m

t1.compareTo(t2): 1

t2.compareTo(t1): -1

t1.compareTo(t1): 0

4 0
2 years ago
A company wants to inform a select list of it's regular customers about a flash sale. Which type of platform will it use to send
blondinia [14]
<h2>Answer :</h2>

In case of Flash Sale, usually company uses Instant messages or SMS. As there are chances customer in most of the cases don’t have access to their emails due to internet unavailability. However SMS can be directed towards customers without the requirements of an internet. In case of SMS, there are companies available that can shoot out targeted SMS based on cities or even an entire country at a very minimal price. Company can provided them there contacts as well as they have a list of numbers from different sources to which they can send instant messages.


5 0
2 years ago
Other questions:
  • The elements in a string type array will be initialized to ____.?
    10·1 answer
  • What was one important academic skill the blogger learned?
    9·1 answer
  • Elias wants to name his data in an excel file. Which step is incorrect?
    13·1 answer
  • Which sector provides scope for multimedia designers?
    10·1 answer
  • Days of the week are represented as three-letter strings ("Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"). Write a javaScript f
    14·1 answer
  • The attack in which the attacker sends a forged packet with the same source IP address and destination IP address in which the v
    10·1 answer
  • "In about 100 words, discuss the technologies that Walmart’s trucking fleet might use to better manage their operations. Include
    7·1 answer
  • Why is accessing a disk block expensive? discuss the time components involved in accessing a disk block. (?
    9·1 answer
  • 1. What are the first tasks the Team Leader (TL) must perform after arriving at the staging area?
    15·1 answer
  • Design and implement an algorithm that gets as input a list of k integer values N1, N2,..., Nk as well as a special value SUM. Y
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!