Which is not a characteristic of an NP-complete problem?

Question

BlackTom AI · Accepted Answer

The question asks which is not a characteristic of an NP-complete problem. 
Note: The provided answer choices are missing, so we cannot compare multiple options. Nevertheless, we can reason about the core concept involved.
A key fact about NP-complete problems is that they are inside NP and are NP-hard, meaning every problem in NP can be reduced to any NP-complete problem in polynomial time. This implies that if any NP-complete problem could be solved in polynomial time, then every problem in NP could be solved in polynomial time (i.e., P = NP). 
Therefore, the statement 'All NP-complete problems can be solved efficiently' is not a characteristic of NP-complete problems under the common assumption that P ≠ NP. In other words, efficiency (polynomial-time solvability) is not guaranteed for NP-complete problems in the general case; it would require a breakthrough that P = NP. 
Common misconceptions sometimes confuse 'verifiable in polynomial time' with 'solvable in polynomial time.' While NP problems have solutions verifiable quickly, NP-complete problems are as hard as the hardest problems in NP, and no known polynomial-time algorithms exist for them unless P = NP. 
If an option claimed that NP-complete problems are always solvable quickly, that would be false; the accurate characteristic is that they are as hard as the hardest problems in NP, with no proven efficient algorithms in the general case unless P equals NP. 
In summary, the problematic claim is the universal efficient solvability of NP-complete problems, which contradicts the widely believed separation between P and NP and the defining properties of NP-completeness.

Which is not a characteristic of an NP-complete problem?

查看解析

登录即可查看完整答案

类似问题

Question at position 17 If you find a polynomial-time solution to even one NP-Complete problem, then every problem in NP can also be solved in polynomial time.TrueFalse题目解析

In the reduction from 3-SAT to Hamiltonian Path, how many nodes are in the graph we construct, assuming the 3-SAT problem has n variables and k clauses?

Which of these problems can be reduced to the Traveling Salesman Problem?

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单