How Do You Spell NP-COMPLETENESS?

Pronunciation: [ˌɛnpˈiːkəmplˈiːtnəs] (IPA)

The spelling of "np-completeness" can be confusing for those not familiar with computer science jargon. It is pronounced as /ɛnˈpiː ˌkɒmplətnəs/ and refers to a complexity class in computational theory. The "np" stands for nondeterministic polynomial time, while "completeness" indicates that these problems are among the hardest in the NP class. Despite its intricate spelling and pronunciation, "np-completeness" is an important concept in computer science and has applications in fields from cryptography to bioinformatics.

NP-COMPLETENESS Meaning and Definition

  1. NP-completeness refers to a concept in computer science and computational complexity theory that measures the difficulty of solving certain computational problems. Specifically, it refers to the classification of a problem as NP-complete (Non-deterministic Polynomial-time complete).

    In the theory of computational complexity, NP refers to the set of decision problems for which the solution can be verified in polynomial time. On the other hand, P refers to the set of decision problems for which the solution can be found in polynomial time. NP-completeness serves as a bridge between NP and P problems by identifying certain problems that are thought to be computationally difficult but still belong to NP.

    A problem is considered NP-complete if it meets two criteria: first, it must belong to the set of problems classified as NP, meaning that any proposed solution can be verified in polynomial time; second, it must be as least as difficult as any other problem in NP. This means that if a solution to any NP-complete problem can be found in polynomial time, then all other NP problems can also be solved in polynomial time. This implies that NP-complete problems are inherently difficult and unlikely to have efficient algorithms to solve them.

    The notion of NP-completeness has profound implications for the field of computational complexity and has been instrumental in understanding the boundaries of computational feasibility. Researchers have extensively studied NP-complete problems to develop approximation algorithms and heuristics that provide practical solutions even if optimal solutions may not be achievable.

Etymology of NP-COMPLETENESS

The term "NP-completeness" is derived from two concepts in computer science: NP and complexity theory.

NP stands for "nondeterministic polynomial time", which is a class of problems in computational complexity theory. These are problems for which a potential solution can be verified quickly but not necessarily found quickly. NP problems are associated with nondeterministic Turing machines.

Completeness, in the context of NP-completeness, refers to a property of problems that are considered to be among the hardest problems in NP. A problem is said to be NP-complete if it is both in the class NP and every other problem in NP can be transformed into it in polynomial time.

The term "NP-completeness" was coined by Stephen Cook in 1971 when he published his landmark paper "The Complexity of Theorem-Proving Procedures". Cook introduced the concept of NP-completeness and defined the class of problems within it.