Computational complexity theory is the branch of the theory of computation that classifies computational problems according to the resources, chiefly time and memory, they require to solve.
Facts
Central QuestionWhether the class of problems whose solutions can be verified quickly, once found, is the same as the class of problems that can be solved quickly in the first place, the P versus NP question, whose answer would settle whether every efficiently checkable problem is also efficiently solvable. 1 Key DebateWhether P equals NP. Stephen Cook and Leonid Levin independently proved in 1971 that practically relevant NP-complete problems exist, problems as hard as any other problem in NP, and the question of whether solving them is really as hard as verifying them remains one of the most important open questions in theoretical computer science, with wide implications should it ever be settled either way. 1 Cross-Tradition Connections
Sources
1. Computational Complexity Theory (Wikipedia)
WikipediaOpening paragraphQuote, Opening paragraph
computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.
1. Computational Complexity Theory (Wikipedia)
WikipediaImportant open problems / P versus NP problemQuote, Important open problems / P versus NP problem
The question of whether P equals NP is one of the most important open questions in theoretical computer science because of the wide implications of a solution.
1. Computational Complexity Theory (Wikipedia)
WikipediaHistoryQuote, History
The field began to flourish in 1971 when Stephen Cook and Leonid Levin proved the existence of practically relevant problems that are NP-complete.
Wikipedia: P versus NP Problem
Wikimedia FoundationIncludes: P versus NP, Context sectionQuote, Includes: P versus NP, Context section
The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources required during computation.
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