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Class in computational complexity theory
{\mathsf {NC}}{\overset {?}{=}}{\mathsf {P}}} More unsolved problems in computer science In computational complexity theory, the class NC (for Nick's
NC_(complexity)
computational complexity of artificial neural networks. The relationship between the TC, NC and the AC hierarchy can be summarized as follows: NC i ⊆ AC i
TC_(complexity)
Model of computational complexity
separate P and NP (see below). Complexity classes defined in terms of Boolean circuits include AC0, AC, TC0, NC1, NC, and P/poly. A Boolean circuit with
Circuit_complexity
In circuit complexity, AC is a complexity class hierarchy. Each class, ACi, consists of the languages recognized by Boolean circuits with depth O ( log
AC_(complexity)
Topics referred to by the same term
state of codon usage biases in genes nc (elliptic function), one of Jacobi's elliptic functions NC (complexity), the set of decision problems decidable
NC
Inherent difficulty of computational problems
Again, there are many complexity classes between the two, such as NL {\displaystyle {\textsf {NL}}} and NC {\displaystyle {\textsf {NC}}} , and it is not
Computational complexity theory
Computational_complexity_theory
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Model of computation
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal
Boolean_circuit
world in which CC and NC are incomparable, and so both containments are strict. E. W. Mayr; A. Subramanian (1992). "The complexity of circuit value and
CC_(complexity)
Computational complexity
received the 1995 Gödel Prize for this work. In circuit complexity, NL can be placed within the NC hierarchy. In Papadimitriou 1994, Theorem 16.1, we have:
NL_(complexity)
Complexity of sending information in a distributed algorithm
In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem
Communication_complexity
Concept in computer science
In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable
BPP_(complexity)
Transformation of one computational problem to another
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently
Reduction_(complexity)
Complexity class (logarithmic space)
In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved
L_(complexity)
Subfield of computational complexity theory
Fine-grained complexity is a subfield of computational complexity theory that studies the time required to solve computational problems, especially those
Fine_grained_complexity
Class in computational complexity theory
In computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be
P-complete
In computational complexity theory, a language B (or a complexity class B) is said to be low for a complexity class A (with some reasonable relativized
Low_(complexity)
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Concept in computational complexity theory
In computational complexity theory, BPL (Bounded-error Probabilistic Logarithmic-space), sometimes called BPLP (Bounded-error Probabilistic Logarithmic-space
BPL_(complexity)
Algorithm characteristic in computations
an algorithm A has good average-case complexity if, after running for tA(n) steps, A can solve all but a nc/(tA(n))ε fraction of inputs of length
Average-case_complexity
Field in logic and theoretical computer science
science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational
Proof_complexity
Method for solving one problem using another
of problem B with different answers. Therefore, for complexity classes within P such as L, NL, NC, and P itself, polynomial-time reductions cannot be
Polynomial-time_reduction
Concept in computational complexity theory
time; that is, if they lie in the complexity class P. In modern terms, it identifies tractable problems with the complexity class P. Formally, to say that
Cobham's_thesis
Apple's network computer prototype
as a "ridiculous device" due to its escalating complexity and cost. Ellison explicitly framed the NC initiative as a proxy war against Microsoft. He
Mac_NC
List of unsolved computational problems
design, and computational theory. What is the relationship between BQP and NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL problem
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Unsolved problem in computational complexity theory
time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem
Graph_isomorphism_problem
Complexity class used in circuit complexity
theoretical computer science, and specifically computational complexity theory and circuit complexity, TC0 (Threshold Circuit) is the first class in the hierarchy
TC0
Algorithm to search the nodes of a graph
could be constructed by a deterministic parallel algorithm, in the complexity class NC. Breadth-first search – Algorithm to search the nodes of a graph
Depth-first_search
Computational complexity class of problems
Chernoff bound. The complexity class is unchanged by allowing error as high as 1/2 − n−c on the one hand, or requiring error as small as 2−nc on the other hand
BQP
Computer scientist
became a fellow of the American Mathematical Society. The complexity class, Nick's Class (NC), of problems quickly solvable on a parallel computer, was
Nick_Pippenger
Largest integer that divides given integers
divisor has a complexity O(T(n) log n). This implies that the fastest known algorithm has a complexity of O(n (log n)2). Previous complexities are valid for
Greatest_common_divisor
Model of computation
circuit complexity Boolean circuit Circuit complexity Circuits over sets of natural numbers The complexity classes NC, AC and TC Quantum circuit and BQP Vollmer
Circuit_(computer_science)
Mathematical function
such that for every positive integer c there exists an integer Nc such that for all n > Nc, | μ ( n ) | < 1 n c . {\displaystyle |\mu (n)|<{\frac {1}{n^{c}}}
Negligible_function
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely
NP-completeness
American-Canadian computer scientist, contributor to complexity theory
mathematics, complexity of higher type functions, complexity of analysis, and lower bounds in propositional proof systems. He named the complexity class NC after
Stephen_Cook
Pseudoscientific argument for the existence of God
arguments against evolutionary explanations: irreducible complexity and specified complexity, asserting that certain biological and informational features
Intelligent_design
The history of numerical control (NC) began when the automation of machine tools first incorporated concepts of abstractly programmable logic, and it continues
History_of_numerical_control
Interstate Highway in North Carolina, United States
River Gorge to U.S. Highway 117 (US 117) and North Carolina Highway 132 (NC 132) in Wilmington. I-40 is the longest Interstate Highway in North Carolina
Interstate 40 in North Carolina
Interstate_40_in_North_Carolina
Type of decision problem in computer science
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input
PSPACE-complete
Type of approximation algorithm
approximation scheme or EPTAS, in which the running time is required to be O(nc) for a constant c independent of ε. This ensures that an increase in problem
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Twin-engine turboprop aircraft
(NC-29, NC-35, and NC-45), one in Texas (NC-50), one in Colorado (NC-51), and four were registered to Beechcraft in Wichita, Kansas (NC-2, NC-8, NC-19
Beechcraft_Starship
Type of computational algorithm
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually
Log-space_reduction
Search problem in quantum mechanics
{\displaystyle QNC^{0}} and N C 0 {\displaystyle NC^{0}} ( Q N C 0 ⊈ N C 0 {\displaystyle QNC^{0}\nsubseteq NC^{0}} ). Given A ∈ F 2 n × n {\displaystyle A\in
Hidden linear function problem
Hidden_linear_function_problem
American mathematician and philosopher (born 1960)
specified complexity and irreducible complexity. The scientific community sees intelligent design—and Dembski's concept of specified complexity—as a form
William_A._Dembski
Topics referred to by the same term
format for nautical charts RNC, a randomized computational complexity class extending NC Nishinippon Broadcasting, a Japanese commercial broadcaster
RNC
Country in Southwestern Europe
facilities are classified by security level, and by degree of management complexity, and often house inmates with different legal statuses, risk levels, and
Portugal
American businessman and politician (born 1979)
Council). Mayoral Runoff As an immigrant himself, Mobolade notes the complexity and difficulty of the legal processes concerning immigration. Mobolade
Yemi_Mobolade
US Marine Corps base in Havelock, North Carolina, United States
at Engelhard, NC (M-116B) 35°29′49″N 076°00′34″W / 35.49694°N 76.00944°W / 35.49694; -76.00944 (M-116B) and one at Holly Ridge, NC (M-116C) 34°30′50″N
Marine Corps Air Station Cherry Point
Marine_Corps_Air_Station_Cherry_Point
Problem that is difficult or impossible to solve
resistance to resolution. Another definition is "a problem whose social complexity means that it has no determinable stopping point". Because of complex
Wicked_problem
Nanoclusters
Kelly J.; Jin, Rongchao (2016). "Emergence of hierarchical structural complexities in nanoparticles and their assembly". Science. 354 (6319): 1580–1584
Monolayer-protected cluster molecules
Monolayer-protected_cluster_molecules
Subexponential bound in computational complexity
quasi-polynomial time. As well as time complexity, some algorithms require quasi-polynomial space complexity, use a quasi-polynomial number of parallel
Quasi-polynomial_growth
Chromatin remodeling complex
exists in subtypes, canonical BAF (cBAF), BAFE (PBAF), and non-canonical BAF (ncBAF), each defined by unique subunit compositions that lead them to have specific
Mammalian SWI/SNF (BAF) complex
Mammalian_SWI/SNF_(BAF)_complex
1965 book by Louis Althusser
single, definitive "original text" problematic. For Young, this textual complexity is not an obstacle to be overcome but is rather the very basis for Althusser's
Reading_Capital
1988 paper by E. W. Dijkstra
Dijkstra's advice. The curricula generally emphasize techniques for managing complexity and preparing for future changes, following Dijkstra's earlier writings
On the Cruelty of Really Teaching Computer Science
On_the_Cruelty_of_Really_Teaching_Computer_Science
Color encoding system for analogue television
mixing, before finally remodulating as FM, at the cost of some added complexity and signal degradation. In its later years, this was no longer a problem
PAL
Implications of Complexity Theory conference, the second time speaking on "The Challenges of Observation, Inquiry, and Measurement in Complexity Theory." Dent
Eric_Dent
American neuroscientist, neurophilosopher, and author
2020). "The Emergence of Informative Higher Scales in Complex Networks". Complexity. 2020: 1–12. arXiv:1907.03902. doi:10.1155/2020/8932526. Hoel, Erik; Klein
Erik_Hoel
Representation of the breadth of the Internet using visual graphics
Retrieved August 8, 2017. "Visual Complexity - Opte Project section". www.visualcomplexity.com. VisualComplexity.com. Archived from the original on December
Opte_Project
Wi-Fi communication standard
Explanation of Basic Operations" (PDF). CWNE Candidate Paper Series. Durham, NC: Certified Wireless Network Professionals. Retrieved 22 October 2024. "Wi-Fi
Opportunistic Wireless Encryption
Opportunistic_Wireless_Encryption
Canadian electrical engineer (born 1940)
files is curated and hosted by the NC State University Libraries. Books, a selection: 1968. On the Feedback Complexity of Automata Ph.D. Thesis. University
Bernard_P._Zeigler
Statement in mathematical combinatorics
any given integers n1, …, nc, there is a number, R(n1, …, nc), such that if the edges of a complete graph of order R(n1, …, nc) are coloured with c different
Ramsey's_theorem
Philosophical concept of social action
Morton’s Hyperobjects), political theory (e.g. William Connolly’s work on complexity and politics), and new materialism (e.g. Rosi Braidotti, Karen Barad)
Assemblage_(philosophy)
Measure in risk analysis
derivation of SIL. Estimation of SIL based on reliability estimates. System complexity, particularly in software systems, making SIL estimation difficult to
Safety_integrity_level
Slave of Thomas Jefferson (c. 1773–1835)
sex and families across the color line in Virginia, 1787-1861. Chapel Hill, NC: University of North Carolina Press. pp. 19–20. ISBN 978-0-8078-5440-2. Phillip
Sally_Hemings
Quantified formulas with real-number variables
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the
Existential theory of the reals
Existential_theory_of_the_reals
2003 American murder trial
attorney, and others. The team had originally planned a film but, given the complexity of the material, expanded their work into a documentary miniseries The
Michael_Peterson_trial
composed of reverse transcriptase enzymes and associated non-coding RNAs (ncRNAs). These complexes function as part of bacterial and archaeal defense mechanisms
Defense associated reverse transcriptase
Defense_associated_reverse_transcriptase
Mathematical game
guarantees. A different derandomization gives a parallel algorithm in the complexity class NC. Finding the optimal choice for the second player in the game, once
Berlekamp_switching_game
American musician (born 1977)
Day, Another Time'". The Huffington Post. Retrieved 2017-04-02. "nc music love army". nc music love army. Retrieved 2017-04-02. "'Songs of Protest' in North
Rhiannon_Giddens
to draw clean energy from Iceland's volcanoes. Scientists report that complexity analysis studies of the Labeled Release experiments of the 1976 Viking
2012_in_science
Algorithm for integer multiplication
{\displaystyle \Omega (n^{2})\,\!} conjecture and other problems in the complexity of computation. Within a week, Karatsuba, then a 23-year-old student,
Karatsuba_algorithm
Independent set which is not a subset of any other independent set
maximal independent set belonged in the Nick's Class complexity zoo of N C 4 {\displaystyle NC_{4}} . That is to say, their algorithm finds a maximal
Maximal_independent_set
Complexity class
In computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum
PostBQP
Measure of similarity and diversity between sets
the complexity to O ( k ) {\displaystyle O(k)} , where k {\displaystyle k} is the number of non-zero attributes. # Pseudocode for O(k) complexity function
Jaccard_index
Type of Turing reduction
In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances
Many-one_reduction
(MIT) "Simulating (logc n)-wise independence in NC" 1988 Shmuel Safra (Weizmann) "On the Complexity of omega-Automata" 1987 John Canny (MIT) "A New Algebraic
Machtey_Award
Task of computing complete subgraphs
that the problem is unlikely to be solvable within the parallel complexity class NC. One can test whether a graph G contains a k-vertex clique, and find
Clique_problem
Type of urban planning design
districts neither of these networks appears in pure form, another level of complexity is introduced that tempers the certainty of analytical findings. Of two
Fused_grid
Theory within consciousness research
IIT's measure of complexity, stating that "there are significant computational barriers to calculating Φ, the measure of high complexity used in IIT. IIT
Integrated_information_theory
Warm-blooded animals with wings and feathers
P.; Jarvis, Erich D.; Mirarab, Siavash; Zhang, Guojie (23 May 2024). "Complexity of avian evolution revealed by family-level genomes". Nature. 629 (8013):
Bird
Optimization problem in computer science
a c/nc-difference to arise, the non-contiguous schedule length must be at least C max n c = 4. {\displaystyle C_{\max }^{nc}=4.} The maximal c/nc-difference
Parallel_task_scheduling
includes at least one vertex from every odd cycle; its parameterized complexity was a longstanding open question. This technique later proved very useful
Iterative_compression
Coming of age literary genre
2017, p. 433. Victorian Fiction as a Bildungsroman: Its Flourishing and Complexity. Cambridge Scholars Publishing. 2019. ISBN 9781527540798. Frank, Joseph
Bildungsroman
Problem in linear algebra
the permanent cannot be computed in polynomial time. In computational complexity theory, a theorem of Valiant states that computing permanents is #P-hard
Computing_the_permanent
American politician (1784–1865)
Muslim scholar whom Owen enslaved, demonstrated an unexpected cultural complexity. Capable of writing in Arabic, Ibn Said lived in Owen's household and
James Owen (American politician)
James_Owen_(American_politician)
Sidi, 1972), is a frequency domain technique utilising the Nichols chart (NC) in order to achieve a desired robust design over a specified region of plant
Quantitative_feedback_theory
"Doing Molecular Biophysics: Finding, Naming, and Picturing Signal Within Complexity", Annual Review of Biophysics, 2013; 42: 1–28, published online February
List of people from Teaneck, New Jersey
List_of_people_from_Teaneck,_New_Jersey
1938 book by C. L. R. James
Jacobins Reader. Durham, NC: Duke University Press. Høgsbjerg, Christian (2014). C.L.R. James in Imperial Britain. Durham, NC: Duke University Press. Høgsbjerg
The_Black_Jacobins
2013 film by Denis Villeneuve
The website's critical consensus states: "Prisoners has an emotional complexity and a sense of dread that makes for absorbing (and disturbing) viewing
Prisoners_(2013_film)
Ethical intimacy with multiple partners
Perfectionists". In Pitzer, Donald E. (ed.). America's Communal Utopias. Chapel Hill, NC: University of North Carolina Press. pp. 253–278. ISBN 978-0807846094. Archived
Polyamory
1937 airship fire in the US
"The American Newsreel: A Complete History, 1911–1967, 2d ed." Jefferson, NC: McFarland & Co., (2006) pp. 142–143 "How Did They Ever Get That" Photoplay
Hindenburg_disaster
2000 video game
character in a single room. Galatea is licensed under the Creative Commons BY-NC-ND 3.0 US license. Galatea alters the typical interactive fiction game mechanics
Galatea_(video_game)
Work of art by Félix Gonzáles-Torres
the 1990s. Ackland Art Museum, University of North Carolina at Chapel Hill, NC. 1 Feb. – 31 Mar. 2013. Cur. Claire Schneider. Catalogue. [Travels to Cheekwood
"Untitled" (Portrait of Ross in L.A.)
"Untitled"_(Portrait_of_Ross_in_L.A.)
Technological innovations that have historically increased productivity
modern electronic device and products. As formulated as Moore's law, the complexity of integrated circuits grew exponentially with the integration of semiconductor
Productivity-improving technologies
Productivity-improving_technologies
Branch of engineering which deals with the optimization of complex processes or systems
growing importance of systems engineering due to increasing technological complexity and the formation of dedicated systems engineering groups. In 1957, E
Industrial_engineering
Logical formulation of recursion
express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular
Fixed-point_logic
Mental illness with multiple personality states
criteria for DID have been criticized for failing to capture the clinical complexity of DID, lacking usefulness in diagnosing individuals with DID (for instance
Dissociative identity disorder
Dissociative_identity_disorder
American actor (1924–1987)
Lentz, Robert J. (2000). Lee Marvin: His Films and Career. Jefferson, NC: McFarland. ISBN 0-7864-0723-9. Marvin, Betty. Tales of a Hollywood Housewife:
Lee_Marvin
1994 multi-role combat aircraft family by Eurofighter
digital signal processor, enabling reductions in the size and system complexity required. The project was given the go-ahead in July 1997 with development
Eurofighter_Typhoon
American actress (born 1952)
Youth Actors: Filmography of Their Entire Careers, 1914-1985. Jefferson, NC: McFarland. p. 7. ISBN 978-0-8995-0247-2. Media related to Mary Badham at
Mary_Badham
travel, tourism, insurance
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