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Mathematic definition
In convex geometry and polyhedral combinatorics, the extension complexity of a convex polytope P {\displaystyle P} is the smallest number of facets among
Extension_complexity
2002 novel by Michael Crichton
computing/scientific community, such as artificial life, emergence (and by extension, complexity), genetic algorithms, and agent-based computing. Fields such as
Prey_(novel)
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
Measure of algorithmic complexity
theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer
Kolmogorov_complexity
Branch of mathematical logic
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic
Descriptive_complexity_theory
Complexity class
In computational complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP. The name is somewhat
FNP_(complexity)
Award for advancements in discrete mathematics
chromatic thresholds of graphs Thomas Rothvoss for his work on the extension complexity of the matching polytope. 2021: Béla Csaba, Daniela Kühn, Allan Lo
Fulkerson_Prize
American author and filmmaker (1942–2008)
scientific community, such as: artificial life, emergence (and by extension, complexity), genetic algorithms, and agent-based computing. In 2004, Crichton
Michael_Crichton
Concept in psychology
humans perceive relevance, cognitive complexity is defined as an extension of the notion of Kolmogorov complexity. It amounts to the length of the shortest
Cognitive_complexity
Attribute of machine learning models
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function
Sample_complexity
Branch of computational complexity theory
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according
Parameterized_complexity
Class of problems solvable in polynomial time
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can
P_(complexity)
This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with
List of computability and complexity topics
List_of_computability_and_complexity_topics
Flat-sided three-dimensional shape
direction not parallel to a face of the polyhedron forms a polygon Extension complexity, the smallest number of facets among convex polytopes that has another
Polyhedron
Computer science award
Rothvoss, Thomas (2017). "The Matching Polytope has Exponential Extension Complexity". Journal of the ACM. 64 (6): 41:1–41:19. arXiv:1311.2369. doi:10
Gödel_Prize
Discrete Fourier transform algorithm
of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n 2 ) {\textstyle O(n^{2})} , which arises
Fast_Fourier_transform
In computational complexity theory, SP 2 is a complexity class, intermediate between the first and second levels of the polynomial hierarchy. A language
S2P_(complexity)
mathematically as instances of the precoloring extension problem on Sudoku graphs. Colbourn, Charles J. (1984), "The complexity of completing partial Latin squares"
Precoloring_extension
Conference in theoretical computer science
2014 Thomas Rothvoss (2014), "The matching polytope has exponential extension complexity" Shafi Goldwasser (2014), "The Cryptographic Lens" (Turing Award
Symposium on Theory of Computing
Symposium_on_Theory_of_Computing
Geometric space with four dimensions
complicated shapes that the full richness and geometric complexity of 4D spaces emerge. A hint of that complexity can be seen in the accompanying 2D animation of
Four-dimensional_space
Logic principle
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands
Extensionality
In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for
Propositional_proof_system
1999 book by Neil Immerman
Descriptive Complexity is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an
Descriptive_Complexity
Belgian physicist
since 2021. In 2023, he received the Gödel Prize for research on extension complexity. Massar, Serge Alexandre (March 2022). "CURRICULUM VITAE" (PDF).
Serge_Massar
Instructions for the x86 microprocessors
FMA4 Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge New Instructions) are SIMD extensions to the x86 instruction
Advanced_Vector_Extensions
Topics referred to by the same term
complexes in Wiktionary, the free dictionary. Complex commonly refers to: Complexity, the behaviour of a system whose components interact in multiple ways
Complex
Ordinal-indexed family of rapidly increasing functions
In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or
Fast-growing_hierarchy
Suite of IETF specifications
The Domain Name System Security Extensions (DNSSEC) is a suite of extension specifications by the Internet Engineering Task Force (IETF) for securing
Domain Name System Security Extensions
Domain_Name_System_Security_Extensions
be performed without one, but are sometimes added due to weaker bases, complexity of a stunt, or an uneven number of athletes. Additional Spot: Additional
List_of_cheerleading_stunts
Discipline for achieving objectives against unpredictability, complexity, and ambiguity
"theory of the business" or natural extension of the mindset or ideological perspective of the organization. Complexity theorists define strategy as the
Strategy
Cryptographic hash function
claimed complexity 252 at the Rump Session of Eurocrypt 2009. However, the accompanying paper, "Differential Path for SHA-1 with complexity O(252)" has
SHA-1
Programming language for automation scripts
generally relatively short and simple. As there is no limit on size or complexity, script is subjective. A few lines of code without branching is probably
Scripting_language
Tool for working with matrices
1257/aer.103.2.585. ISSN 0002-8282. Vazirani, Vijay V. (2020-10-14). "An Extension of the Birkhoff-von Neumann Theorem to Non-Bipartite Graphs". arXiv:2010
Birkhoff_algorithm
other theoretical investigations into computational complexity and universality. Another extension is the formulation of quantum random-access Turing machines
Random-access_Turing_machine
Generic-case complexity is a subfield of computational complexity theory that studies the complexity of computational problems on "most inputs". Generic-case
Generic-case_complexity
Hashing technique
log N ) {\displaystyle O(\log N)} or O ( N ) {\displaystyle O(N)} complexities respectively; and in every iteration, which happens in clockwise manner
Consistent_hashing
than just paths, however they are intractable to evaluate. A further extension allowing both disjunctions (like union of conjunctive queries) and two-way
Regular_path_query
Given more time, a Turing machine can solve more problems
In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. Informally
Time_hierarchy_theorem
Theory
Public Opinion Quarterly, 34, 184–190. Pavlik, J.V. (1988). Audience complexity as a component of campaign planning. Public Relations Review, 14, 12–20
Situational_theory_of_publics
Concept in mathematics
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems
Conservative_extension
Objective function for greedy algorithms
In combinatorics, a branch of mathematics, a weighted matroid is a matroid endowed with a function that assigns a weight to each element. Formally, let
Weighted_matroid
Practice of leading the work of a team to achieve goals and criteria at a specified time
for project management to be effective. Complexity can be: Structural complexity (also known as detail complexity, or complicatedness), i.e. consisting
Project_management
Lossy audio compression format
commonly using the filename extension .m4a. The basic profile of AAC (both MPEG-4 and MPEG-2) is called AAC-LC (Low Complexity). It is widely supported in
Advanced_Audio_Coding
London Underground line
(UERL) took over the line, it was renamed the Piccadilly line. Subsequent extensions were made to Cockfosters, Hounslow West and Uxbridge in the early 1930s
Piccadilly_line
Method of determining a point in 3D space
of some parameters. This means that both the computation time and the complexity of the operations involved may vary between the different methods. Each
Triangulation (computer vision)
Triangulation_(computer_vision)
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
Book by Stephen Wolfram
of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops
A_New_Kind_of_Science
Hair that artificially adds length to human hair
commonly known as hair extensions, hair weaves, or fake hair, are cosmetic treatments which add length to human hair. Hair extensions are usually clipped
Artificial_hair_integrations
Type of database query
considered part of the input. The complexity of this problem is usually referred to as combined complexity, while the complexity of the problem of evaluating
Conjunctive_query
Pencil and paper connection game
filled in, the player who has taken the most squares is the winner. An extension of Gale, called Qua, is played by three players on a 3D game board cube
Shannon_switching_game
Mathematical theorem
series to a bracket series. Obtain the complexity index, formula parameters and series coefficient function. Complexity index is the number of integrand sums
Ramanujan's_master_theorem
modifications such as Montgomery's prime pairing (1978) and the Brent-Suyama extension. A more efficient "stage 2" method uses polynomial multiplication implemented
Algebraic-group factorisation algorithm
Algebraic-group_factorisation_algorithm
Aspect of timekeeping
seven-week extension of DST would yield an additional $30 million for 7-Eleven stores, and the National Golf Foundation estimated the extension would increase
Analysis of daylight saving time
Analysis_of_daylight_saving_time
Pattern-finding real-time card game
Kamalika; Godfrey, Brighten; Ratajczak, David; Wee, Hoeteck (2003). On the Complexity of the Game of Set (PDF) (Technical report). Archived (PDF) from the original
Set_(card_game)
Instruction set extension by Intel
AVX-512 are 512-bit extensions to the 256-bit Advanced Vector Extensions SIMD instructions for x86 instruction set architecture (ISA) proposed by Intel
AVX-512
Two-dimensional Turing machine with emergent behavior
hdl:2027.42/26022. Gajardo, A.; Moreira, A.; Goles, E. (15 March 2002). "Complexity of Langton's ant" (PDF). Discrete Applied Mathematics. 117 (1–3): 41–50
Langton's_ant
Correspondence between quantum channels and quantum states
\oplus 0} need to be designed. The channel R 0 {\displaystyle R_{0}} , an extension of the channel R, contains three Kraus operators: K 0 = [ p ρ t , 0 ]
Choi–Jamiołkowski_isomorphism
Approximate distinct counting algorithm
accuracy (standard error) of 2%, using 1.5 kB of memory. HyperLogLog is an extension of the earlier LogLog algorithm, itself deriving from the 1984 Flajolet–Martin
HyperLogLog
Cross-platform graphics API
(GPU) vendors may provide additional functionality in the form of extensions. Extensions may introduce new functions and new constants, and may relax or
OpenGL
List Wikipedia article
(1712), Bailey's dictionary (1726), Martin's dictionary (1749). Some complexities surrounding the English word's history are discussed in Hensleigh Wedgwood
List of English words of Arabic origin (A–B)
List_of_English_words_of_Arabic_origin_(A–B)
S2CID 2634447 Junosza-Szaniawski, Konstanty; Rzążewski, Paweł (2011), "On the complexity of exact algorithm for L(2,1)-labeling of graphs", Information Processing
Radio_coloring
Graph polynomial generating numbers of matchings
Courcelle, B.; Makowsky, J. A.; Rotics, U. (2001), "On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic"
Matching_polynomial
Algorithm used for pathfinding and graph traversal
major practical drawback is its O ( b d ) {\displaystyle O(b^{d})} space complexity where d is the depth of the shallowest solution (the length of the shortest
A*_search_algorithm
Problem in computer science
Unsolved problem in computer science What is the Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science
Square-root_sum_problem
Mathematical theory
into a slipknot and effectively erase the knot, or introduce additional complexity that is not present in the initial curve. In such cases, it may be beneficial
Open_knot_theory
Equivalence of average-case and expected complexity
In computational complexity theory, Yao's principle (also called Yao's minimax principle or Yao's lemma) relates the performance of randomized algorithms
Yao's_principle
Extension of nondeterministic tree automaton
Extension of nondeterministic tree automaton
Alternating_tree_automata
Description of a system using mathematical concepts and language
important to get an accurate estimate of the probability. In general, model complexity involves a trade-off between simplicity and accuracy of the model. Occam's
Mathematical_model
Mathematical algorithm
capacitance, electrostatic internal energy of molecules, etc.). Some notable extensions include: The WoS method can be modified to solve more general problems
Walk-on-spheres_method
1978 extension of Toronto subway line
twice: first in 1964, to build extensions of the Bloor–Danforth line and then again in 1965, to build a northerly extension of the Yonge Street branch of
Spadina_subway_line
Problem of determining if a Boolean formula could be made true
NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization
Boolean satisfiability problem
Boolean_satisfiability_problem
Term in mathematical logic
finite model in which a given sentence is true. By a result in descriptive complexity, a set of natural numbers is a spectrum if and only if it can be recognized
Spectrum_of_a_sentence
Computational benchmark
quantum cases, complexity swells with increasing problem size. As an extension of classical computational complexity theory, quantum complexity theory considers
Quantum_supremacy
Task of transforming a deterministic finite automaton
checking whether it is present), this algorithm can be implemented with time complexity O ( n + m ) {\displaystyle O(n+m)} , where n {\displaystyle n} is the
DFA_minimization
Set of all possible values of a system
November 2019. Zhang, Weixong (1999). State-space search: algorithms, complexity, extensions, and applications. Springer. ISBN 978-0-387-98832-0. Abbeel, Pieter
State space (computer science)
State_space_(computer_science)
Security-related instruction code processor extension
Intel Software Guard Extensions (SGX) is a set of instruction codes implementing trusted execution environment that are built into some Intel central processing
Software_Guard_Extensions
Museum in Guangzhou, China
using openwork techniques. This vessel showcases extraordinary decorative complexity: the body displays a triple-tiered scheme featuring raised relief whirl
Nanyue_King_Museum
In logic, defining a new symbol
logic, more specifically in the proof theory of first-order theories, an extension by definition formalizes the introduction of a new symbol by means of
Extension_by_definition
Signal processing design process
requirement Computational complexity Technology required The required frequency response is an important parameter. The steepness and complexity of the response
Filter_design
Image file format with multiple editions
builds over JIF to solve some of JIF's limitations, including unnecessary complexity, component sample registration, resolution, aspect ratio, and color space
JPEG_File_Interchange_Format
Class of computational problem
ISBN 978-1-118-58537-5. Garey, M. R.; Johnson, D. S.; Sethi, Ravi (1976). "The complexity of flowshop and jobshop scheduling". Mathematics of Operations Research
Flow-shop_scheduling
Mathematical investigation of Sudoku
in particular Figure 7, p. 7. Yato, Takayuki; Seta, Takahiro (2003). "Complexity and Completeness of Finding Another Solution and Its Application to Puzzles"
Mathematics_of_Sudoku
is cottage cheese. The term 'yellow gravy' might not do justice to the complexity of flavor you get from layering nine spices, some of them whole, with
List_of_Kashmiri_dishes
Mnemonic, giving criteria to guide in the setting of objectives
Bilson, Andy (2013). Social Work Management and Leadership : Managing Complexity with Creativity. Routledge. pp. 84–85. ISBN 978-1-135-24705-8. Retrieved
SMART_criteria
Computer network protocol
registries, strove to keep the protocol as simple as possible, since complexity was considered one of the reasons why previous attempts, such as CRISP
Registration Data Access Protocol
Registration_Data_Access_Protocol
Diagram that shows all possible logical relations between a collection of sets
Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing
Venn_diagram
Every square matrix with positive entries can be written in a certain standard form
doi:10.1063/1.4915289. S2CID 119707158. Gurvits, Leonid (2004). "Classical complexity and quantum entanglement". Journal of Computational Science. 69 (3): 448–484
Sinkhorn's_theorem
Automated planner
and B. Nebel (1995). Complexity results for SAS+ planning. Computational Intelligence, 11:625-656. T. Bylander (1991). Complexity results for planning
Stanford Research Institute Problem Solver
Stanford_Research_Institute_Problem_Solver
Class of algorithms which use a moving line to solve geometrical problems
application of the approach had led to a breakthrough in the computational complexity of geometric algorithms when Shamos and Hoey presented algorithms for
Sweep_line_algorithm
Simplicial complex in Euclidean geometry
triangulations realizable on a fixed point set, highlighting the exponential complexity of these structures. Every triangulation of any set P {\displaystyle {\mathcal
Point-set_triangulation
Mathematical model
was a breakthrough result that spurred extensive research into various extensions, including stopwatches, real-time tasks, cost functions, and timed games
Timed_automaton
Set-to-real map with diminishing returns
increase in the items one buys. Submodular functions model notions of complexity, similarity and cooperation when they appear in minimization problems
Submodular_set_function
West African population history
S2CID 198759644. Brass, Michael (2007). "Reconsidering the emergence of social complexity in early Saharan pastoral societies, 5000 – 2500 B.C." Sahara (Segrate
Population history of West Africa
Population_history_of_West_Africa
Mathematical principle
under certain conditions with assurance that the extension will introduce no contradiction. Extension by definitions is perhaps the best-known approach
Extension by new constant and function names
Extension_by_new_constant_and_function_names
Necessary and sufficient condition for a formal language to be regular
1.5. Brzozowski, Janusz; Szykuła, Marek; Ye, Yuli (2018). "Syntactic Complexity of Regular Ideals". Theory of Computing Systems. 62 (5): 1175–1202. doi:10
Myhill–Nerode_theorem
United States Air Force software development division
among Kessel Run staff with emerging bureaucracy and increasing technical complexity. The Air Force's Deputy Chief Information Officer, Lauren Knausenberger
Kessel_Run
Study of organisms and their environment
S2CID 40349801. Loehle, C. (2004). "Challenges of ecological complexity". Ecological Complexity. 1 (1): 3–6. Bibcode:2004EcoCm...1....3.. doi:10.1016/j.ecocom
Ecology
Study of computation
models of computation. The second question is addressed by computational complexity theory, which studies the time and space costs associated with different
Computer_science
Field in mathematics similar to the real numbers
(n)} is big Omega notation. This shows that both the time complexity and the space complexity of quantifier elimination are intrinsically double exponential
Real_closed_field
History of crystallography to 1895
In 1900 three-circle goniometers were designed but their high cost and complexity meant that they were not widely adopted. In the 17th century optical microscopes
History of crystallography before X-rays
History_of_crystallography_before_X-rays
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
Boy/Male
Indian, Punjabi, Sikh
Philosophy; Extensive Reflection
Girl/Female
Biblical
Changing, extension of the mouth.
Girl/Female
Indian
Extensive; Broad
Girl/Female
Biblical
Bed, extension, a coal.
Boy/Male
Arabic, Muslim
Extension; Excess
Boy/Male
Hindu
Abundance, Powerful, Extensive
Biblical
changing; extension of the mouth
Boy/Male
Tamil
Abundance, Powerful, Extensive
Boy/Male
Indian, Sanskrit
Development; Expansion
Boy/Male
Sikh
Philosophy, Extensive reflection, Contemplation
Girl/Female
Tamil
Tension
Girl/Female
Indian
Tension
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Extension; Heap; Plenty; Abundance
Boy/Male
Hindu, Indian
Thought; Tension
Boy/Male
Arabic
Fragrant; Wide; Extensive
Biblical
bed; extension; a coal
Girl/Female
Biblical
Large, extensive.
Boy/Male
Indian, Punjabi, Sikh
Philosophy; Extensive Reflection
Boy/Male
Hindu, Indian, Marathi
Extensive; King
Biblical
large; extensive
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
Girl/Female
British, Christian, English, French, Latin
Joy; Popular Medieval Form of the Name Letitia; Gladness; Happiness
Girl/Female
Indian, Tamil
Terrify; Scaring Others
Boy/Male
Tamil
Ilandevan | இலாநà¯à®¤à¯‡à®µà®¨
Young master
Boy/Male
Bengali, Hindu, Indian, Marathi, Punjabi, Sikh
New; Cleaned
Girl/Female
Arabic, Muslim
Kindness; Politeness
Male
Russian
(Макар) Short form of Russian Makariy, MAKAR means "blessed."
Girl/Female
American, Australian, British, Chinese, English, Hebrew, Indian
God has Answered; Modern Name Based on Jane or Jean; Based on Janai; Female Version of John; The Lord is Gracious; Wild Flower
Male
German
Variant form of Old High German Lewenhart, LEONHARDT means "lion-strong."
Girl/Female
Indian
Sky, Heavens
Girl/Female
Arabic, Muslim, Pashtun
Lal - Ruby; Zar - Golden
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
EXTENSION COMPLEXITY
v. t.
A written engagement on the part of a creditor, allowing a debtor further time to pay a debt.
n.
The developed result of an indicated operation; as, the expansion of (a + b)2 is a2 + 2ab + b2.
n.
The collective attributes, qualities, or marks that make up a complex general notion; the comprehension, content, or connotation; -- opposed to extension, extent, or sphere.
n.
A straining, stretching, or bending; the state of being strained; as, the intension of a musical string.
a.
The act of stretching or straining; the state of being stretched or strained to stiffness; the state of being bent strained; as, the tension of the muscles, tension of the larynx.
n.
Extension.
v. t.
The straightening of a limb, in distinction from flexion.
n.
Extension.
a.
Incapable of expansion, enlargement, or extension.
v. t.
The act of extending or the state of being extended; a stretching out; enlargement in breadth or continuation of length; increase; augmentation; expansion.
v. i.
To admit extension.
a.
Suited for, or capable of, extension; extensible.
a.
Expansive force; the force with which the particles of a body, as a gas, tend to recede from each other and occupy a larger space; elastic force; elasticity; as, the tension of vapor; the tension of air.
v. t.
Capacity of a concept or general term to include a greater or smaller number of objects; -- correlative of intension.
a.
The force by which a part is pulled when forming part of any system in equilibrium or in motion; as, the tension of a srting supporting a weight equals that weight.
n.
Want of extension; unextended state.
n.
Enlargement or extension of business transactions; esp., increase of the circulation of bank notes.
n.
That which is expanded; expanse; extend surface; as, the expansion of a sheet or of a lake; the expansion was formed of metal.
n.
Unlimited extension.
a.
Having wide extent; of much superficial extent; expanded; large; broad; wide; comprehensive; as, an extensive farm; an extensive lake; an extensive sphere of operations; extensive benevolence; extensive greatness.