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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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 Classification
Pure or AppliedBoth / Interdisciplinary 1 Connections
Associated With
Includes
Source Andrey Kolmogorov (Wikipedia)
Source Blum's speedup theorem, Wikipedia
Source Function Problem (Wikipedia)
Source Hartmanis-Stearns Conjecture (Wikipedia)
Source Immerman-Szelepcsenyi theorem, Wikipedia
Source Juris Hartmanis (Wikipedia)
Source NP-intermediate (Wikipedia)
Source Leslie Valiant (Wikipedia)
Source Manindra Agrawal (Wikipedia)
Source Manuel Blum (Wikipedia)
Source Mike Paterson (Wikipedia)
Source Neil Immerman (Wikipedia)
Additional Source Wikipedia: P versus NP ProblemContext section
Source Patrick C. Fischer (Wikipedia)
Source PCP theorem, Wikipedia
Source Richard E. Stearns (Wikipedia)
Source Richard Lipton (Wikipedia)
Source Richard M. Karp (Wikipedia)
Source Rūsiņš Mārtiņš Freivalds (Wikipedia)
Source Sanjeev Arora (Wikipedia)
Source Savitch's theorem, Wikipedia
Source Seinosuke Toda (Wikipedia)
Source Sensitivity theorem (Wikipedia)
Source Sheila Greibach (Wikipedia)
Source Sipser-Lautemann theorem, Wikipedia
Source Space hierarchy theorem, Wikipedia
Source Subhash Khot (Wikipedia)
Source Toda's theorem, Wikipedia
Source Unique Games Conjecture (Wikipedia)
Source Valiant-Vazirani theorem, Wikipedia
Source Vijay Vazirani (Wikipedia)
Source Volker Strassen (Wikipedia)
Source Walter Savitch (Wikipedia)
Sources
1. Computational Complexity Theory (Wikipedia)
WikipediaHistory section
The beginning of systematic studies in computational complexity is attributed to the seminal 1965 paper "On the Computational Complexity of Algorithms" by Juris Hartmanis and Richard E
Opening paragraph
computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.
Lead section, pure or applied classification
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.
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.
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.
In Group: Information, Coding and Complexity, lead paragraph
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.
View the Source 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.
View the Source Juris Hartmanis (Wikipedia)
Includes: Juris Hartmanis, Lead, Turing Award citationQuote, Includes: Juris Hartmanis, Lead, Turing Award citation
established the foundations for the field of computational complexity theory
View the Source Richard E. Stearns (Wikipedia)
Includes: Richard E. Stearns, Lead, Turing Award citationQuote, Includes: Richard E. Stearns, Lead, Turing Award citation
foundations for the field of computational complexity theory
View the Source Subhash Khot (Wikipedia)
Includes: Subhash Khot, LeadQuote, Includes: Subhash Khot, Lead
Khot has contributed to the field of computational complexity
View the Source Sanjeev Arora (Wikipedia)
Includes: Sanjeev Arora, Career, textbookQuote, Includes: Sanjeev Arora, Career, textbook
He is a coauthor (with Boaz Barak) of the book Computational Complexity: A Modern Approach.
View the Source Richard Lipton (Wikipedia)
Includes: Richard Lipton, Karp-Lipton theoremQuote, Includes: Richard Lipton, Karp-Lipton theorem
if SAT can be solved by Boolean circuits with a polynomial number of logic gates, then the polynomial hierarchy collapses to its second level
View the Source Manindra Agrawal (Wikipedia)
Includes: Manindra Agrawal, CareerQuote, Includes: Manindra Agrawal, Career
time that has been proven to be polynomial in n
View the Source Vijay Vazirani (Wikipedia)
Includes: Vijay Vazirani, ResearchQuote, Includes: Vijay Vazirani, Research
together with work on computational complexity theory, cryptography, and algorithmic game theory
View the Source Neil Immerman (Wikipedia)
Includes: Neil Immerman, LeadQuote, Includes: Neil Immerman, Lead
database theory, and computational complexity theory
View the Source Manuel Blum (Wikipedia)
Includes: Manuel Blum, LeadQuote, Includes: Manuel Blum, Lead
the foundations of computational complexity theory
View the Source Seinosuke Toda (Wikipedia)
Includes: Seinosuke Toda, Lead, Toda's theoremQuote, Includes: Seinosuke Toda, Lead, Toda's theorem
for proving Toda's theorem in computational complexity theory
View the Source Walter Savitch (Wikipedia)
Includes: Walter Savitch, Lead, complexity class NLQuote, Includes: Walter Savitch, Lead, complexity class NL
was best known for defining the complexity class NL
View the Source Leslie Valiant (Wikipedia)
Includes: Leslie Valiant, Research and careerQuote, Includes: Leslie Valiant, Research and career
Among his many contributions to Complexity Theory, he introduced the notion of #P-completeness
View the Source Sheila Greibach (Wikipedia)
Includes: Sheila Greibach, Early career, research interestsQuote, Includes: Sheila Greibach, Early career, research interests
Her areas of interest and research include Theoretical computer science, Computational complexity
View the Source Mike Paterson (Wikipedia)
Includes: Mike Paterson, LeadQuote, Includes: Mike Paterson, Lead
especially in the design and analysis of algorithms and computational complexity
View the Source Rūsiņš Mārtiņš Freivalds (Wikipedia)
Includes: Rūsiņš Mārtiņš Freivalds, Lead, theory of computationQuote, Includes: Rūsiņš Mārtiņš Freivalds, Lead, theory of computation
fundamental contributions to the theory of computation, probabilistic algorithms, inductive inference, and quantum computing
View the Source Volker Strassen (Wikipedia)
Includes: Volker Strassen, ResearchQuote, Includes: Volker Strassen, Research
Strassen's pioneering work contributed to probability theory, functional analysis, mathematical statistics, algorithm design, and computational complexity theory.
View the Source Richard M. Karp (Wikipedia)
Includes: Richard M. Karp, Work, branchQuote, Includes: Richard M. Karp, Work, branch
he published a landmark paper in complexity theory
View the Source Patrick C. Fischer (Wikipedia)
Includes: Patrick C. Fischer, ResearchQuote, Includes: Patrick C. Fischer, Research
Fischer was an early leader in the field of computational complexity
View the Source Unique Games Conjecture (Wikipedia)
Wikimedia FoundationIncludes: Unique Games Conjecture, Lead sentenceQuote, Includes: Unique Games Conjecture, Lead sentence
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in
View the Source Space hierarchy theorem, Wikipedia
Includes: Space Hierarchy Theorem, Lead sentenceQuote, Includes: Space Hierarchy Theorem, Lead sentence
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nond
View the Source Function Problem (Wikipedia)
Includes: Function Problem, Lead sentenceQuote, Includes: Function Problem, Lead sentence
In computational complexity theory, a function problem is a computational problem where a single output is expected for every inpu
View the Source Savitch's theorem, Wikipedia
Includes: Savitch's Theorem, Lead sentenceQuote, Includes: Savitch's Theorem, Lead sentence
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministi
View the Source Immerman-Szelepcsenyi theorem, Wikipedia
Blum's speedup theorem, Wikipedia
Includes: Blum's Speedup Theorem, Lead sentenceQuote, Includes: Blum's Speedup Theorem, Lead sentence
In computational complexity theory, Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about th
View the Source Sipser-Lautemann theorem, Wikipedia
Toda's theorem, Wikipedia
Includes: Toda's Theorem, Lead sentenceQuote, Includes: Toda's Theorem, Lead sentence
Toda's theorem is a result in computational complexity theory that was proven by Seinosuke Toda in his paper "PP is as Hard as the
View the Source Valiant-Vazirani theorem, Wikipedia
PCP theorem, Wikipedia
Includes: PCP Theorem, Lead sentenceQuote, Includes: PCP Theorem, Lead sentence
In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision pr
View the Source Andrey Kolmogorov (Wikipedia)
Includes: Andrey Kolmogorov, Lead paragraphQuote, Includes: Andrey Kolmogorov, Lead paragraph
He also gave fundamental contributions to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, functional analysis, algorithmic information theory and computational complexity.
View the Source NP-intermediate (Wikipedia)
Includes: Ladner's Theorem, Lead paragraphQuote, Includes: Ladner's Theorem, Lead paragraph
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI.
View the Source Hartmanis-Stearns Conjecture (Wikipedia)
Includes: Hartmanis-Stearns Conjecture, Lead sectionQuote, Includes: Hartmanis-Stearns Conjecture, Lead section
who posed it in a 1965 paper that founded the field of computational complexity theory (earning them the 1993 ACM Turing Award).
View the Source Sensitivity theorem (Wikipedia)
Includes: Sensitivity Theorem, Lead sectionQuote, Includes: Sensitivity Theorem, Lead section
In computational complexity, the sensitivity theorem, proved by Hao Huang
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.