Why P = NP is considered an open problem? P- Polynomial time solving NP- Non deterministic...
- Why P = NP is considered an open problem?
P- Polynomial time solving
NP- Non deterministic Polynomial time solving
Homework Answers
The problem P vs NP is a typical problem in the field of computer science which remains unsolved. The statement for this problem is like that it seeks to answer the question that if we have a problem whose solution is verified quickly, is also solvable quickly. A huge price exists for solving this problem. It is considered a highly notorious problem and being left unsolved has given it a name called an open problem. However, researchers aiming to solve the problem have found very deep insights to it.
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Why P = NP is considered an open problem?
P- Polynomial time solving
NP- Non deterministic...
If a deterministic polynomial algorithm is found for any NP-complete problem, then it must be the...
If a deterministic polynomial algorithm is found for any NP-complete problem, then it must be the case that P + NP. O True False
All decision problems (i.e.language membership problems), which are verifiable in polynomial time by a deterministic Turing...
All decision problems (i.e.language membership problems), which are verifiable in polynomial time by a deterministic Turing machine are called NP problems. Further, these problems can be solved by a non-deterministic Turing machine in a polynomial time and in exponential time by a deterministic Turing machine. Do we have a decision problem that is not verifiable by a deterministic Turing machine in polynomial time but decidable?
2. Describe why finding a polynomial-time algorithm for a NP-complete problem would answer the question if...
2. Describe why finding a polynomial-time algorithm for a NP-complete problem would answer the question if P = NP. What would the answer be? (7-10 sentences minimum)
1) What is your INFORMED opinion on the NP problems? Does a deterministic polynomial time algorit...
1) What is your INFORMED opinion on the NP problems? Does a deterministic polynomial time algorithm exist or not? Your answer should be a well-thought out and informed argument consisting of several paragraphs at least. No credit for poor grammar and simplistic answers. Your argument should be convincing and strong. EXPLAIN IN DETAIL
Question 1 The following statements illustrate which concept below? var1 = 1 while var1 != 0: var1 = var1+ 1 A. A P complex problem. B. A deterministic problem. C. An NP problem. D. The halting probl...
Question 1 The following statements illustrate which concept below? var1 = 1 while var1 != 0: var1 = var1+ 1 A. A P complex problem. B. A deterministic problem. C. An NP problem. D. The halting problem. Question 2 If a function is computable, A. both a Turing machine and a Bare Bones Language program can solve it . B. a Turing machine can solve it, but a Bare Bones Language program cannot . C. a Turing machine cannot solve...
(complexity) prove: if P=NP, then there's an algorithm with a polynomial running time for the fol...
(complexity) prove: if P=NP, then there's an algorithm with a polynomial running time for the following problem: input: a boolean formula φ output: a satisfying assignment of φ if φ satisfiable. if φ not satisfiable, a "no" will be returned. explanation: the algorithm accepts φ as an input (boolean formula). if φ doesn't have a satisfiable assignment, a "no" is returned. if φ does have a satisfiable assignment, one of the satisfying assignment is returned,. so we assign 0 or...
Claim: It is known that any NP-complete problem will require exponential time (that is, a polynomial...
Claim: It is known that any NP-complete problem will require exponential time (that is, a polynomial time algorithm for it is known to be impossible). TRUE or FALSE?
4. a) Define the concept of NP-Completeness B) Show that there is a polynomial time algorithm...
4. a) Define the concept of NP-Completeness B) Show that there is a polynomial time algorithm that finds a longest path in a directed graph, under the condition that A is NP-complete and A has a polynomial time algorithm.
Prove that IS is in NP. If a language L polynomial-time reduces to IS, must L...
Prove that IS is in NP. If a language L polynomial-time reduces to IS, must L be in NP? Prove your answer.
1. Suppose that problem A polynomial-time reduces to problem B, in other words, we can find a polynomial time algorithm that uses solutions to instances of problem B (given by an oracle - aka “fairy g...
1. Suppose that problem A polynomial-time reduces to problem B, in other words, we can find a polynomial time algorithm that uses solutions to instances of problem B (given by an oracle - aka “fairy godmother”) to solve problem A. 1a. If problem A can be shown to be NP-complete, what does that tell us about problem B? 1b. If problem B can be shown to be in P, what does that tell us about problem A?
If a deterministic polynomial algorithm is found for any NP-complete problem, then it must be the case that P + NP. O True False
2. Describe why finding a polynomial-time algorithm for a NP-complete problem would answer the question if P = NP. What would the answer be? (7-10 sentences minimum)
Claim: It is known that any NP-complete problem will require exponential time (that is, a polynomial time algorithm for it is known to be impossible). TRUE or FALSE?
4. a) Define the concept of NP-Completeness B) Show that there is a polynomial time algorithm that finds a longest path in a directed graph, under the condition that A is NP-complete and A has a polynomial time algorithm.
Prove that IS is in NP. If a language L polynomial-time reduces to IS, must L be in NP? Prove your answer.
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