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A proper complexity function is a function f mapping natural numbers to natural numbers such that: f is nondecreasing; there exists a k-string Turing machine
Proper_complexity_function
Set of problems in computational complexity theory
There are, however, many complexity classes defined in terms of other types of problems (e.g. counting problems and function problems) and using other
Complexity_class
Grammatical concept
romanization for Mandarin Chinese, capitalization is used to mark proper names, with some complexities because of different Chinese classifications of nominal types
Proper_noun
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Unit of measurement
Early and easy function points – Adjusts for problem and data complexity with two questions that yield a somewhat subjective complexity measurement; simplifies
Function_point
Function computable with bounded loops
time complexity is bounded above by a primitive recursive function of the input size. It is hence not particularly easy to devise a computable function that
Primitive_recursive_function
Collection of sets in mathematics that can be defined based on a property of its members
are proper classes in many formal systems. In Quine's set-theoretical writing, the phrase "ultimate class" is often used instead of the phrase "proper class"
Class_(set_theory)
There is an infinite hierarchy of generic complexity classes. More precisely for a proper complexity function f, G e n ( f ) ⊊ G e n ( f 3 ) {\displaystyle
Generic-case_complexity
Function used in computer cryptography
computational complexity theory, specifically the theory of polynomial time problems. This has nothing to do with whether the function is one-to-one;
One-way_function
Unsolved problem in computer science
functions, and subsets. The languages in the polynomial hierarchy, PH, correspond to all of second-order logic. Thus, the question "is P a proper subset
P_versus_NP_problem
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)
Class in computational complexity theory
{\displaystyle {\mathsf {NC}}} hierarchy proper? More unsolved problems in computer science One major open question in complexity theory is whether or not every
NC_(complexity)
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
Argument by proponents of intelligent design
Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were
Irreducible_complexity
Implicit computational complexity (ICC) is a subfield of computational complexity theory that characterizes programs by constraints on the way in which
Implicit computational complexity
Implicit_computational_complexity
Set of all things that may be the input of a mathematical function
the unknown function(s) sought. For example, it is sometimes convenient in set theory to permit the domain of a function to be a proper class X, in which
Domain_of_a_function
Deterministic time, in computational complexity theory
a certain amount of deterministic time. Any proper complexity function can be used to define a complexity class, but only certain classes are useful to
DTIME
Numerical method that reduces the complexity of computationally intensive simulations
The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational
Proper orthogonal decomposition
Proper_orthogonal_decomposition
Problem a computer might be able to solve
strings using binary encoding. This is important since the complexity is expressed as a function of the length of the input representation. A decision problem
Computational_problem
Mapping arbitrary data to fixed-size values
the hash function should be computable with minimum latency and secondarily in a minimum number of instructions. Computational complexity varies with
Hash_function
Class of computational complexity
the complexity classes NL, P, NP, PH, EXPTIME and EXPSPACE (we use here ⊂ {\displaystyle \subset } to denote strict containment, meaning a proper subset
PSPACE
Framework for scoring a behavior's complexity
The model of hierarchical complexity (MHC) is a framework for scoring how complex a behavior is, such as verbal reasoning or other cognitive tasks. It
Model of hierarchical complexity
Model_of_hierarchical_complexity
statistics, the complexity index of a function denotes the level of informational content, which in turn affects the difficulty of learning the function from examples
Complexity_index
Algorithm for finding sub-text location(s) inside a given sentence in Big O(n) time
complexity O(n), where n is the length of S and the O is big-O notation. Except for the fixed overhead incurred in entering and exiting the function,
Knuth–Morris–Pratt_algorithm
Algorithm for finding a zero of a function
bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists
Bisection_method
Subroutine call performed as final action of a procedure
call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such
Tail_call
Cryptographic primitive
construction reduces the problem of finding a proper hash function to finding a proper compression function. A second preimage attack (given a message m 1 {\displaystyle
One-way_compression_function
Methodic assignment of colors to elements of a graph
repeated on the remaining subgraph until no vertices remain. The worst-case complexity of DSatur is O ( n 2 ) {\displaystyle O(n^{2})} , where n {\displaystyle
Graph_coloring
Algorithmic complexity class
time, where p(n) is a polynomial function of n. EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more
EXPTIME
Function in algebraic graph theory
a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff
Chromatic_polynomial
Computation model defining an abstract machine
following five operations (cf. p. 52–53): The arithmetic functions +, −, ×, where − indicates "proper" subtraction: x − y = 0 if y ≥ x. Any sequence of operations
Turing_machine
Halting probability of a random computer program
valid program can be obtained as a proper extension of another valid program. Suppose that F is a partial function that takes one argument, a finite binary
Chaitin's_constant
Set whose elements all belong to another set
It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called
Subset
Integral expressing the amount of overlap of one function as it is shifted over another
a mathematical operation on two functions f {\displaystyle f} and g {\displaystyle g} that produces a third function f ∗ g {\displaystyle f*g} , as the
Convolution
Sequence of random variables
formalized his definition of a proper selection rule for sub-sequences, but in 1940 Alonzo Church defined it as any recursive function which having read the first
Random_sequence
Technique to make a model more generalizable and transferable
_{i=1}^{N}V(f_{n}({\hat {x}}_{i}),{\hat {y}}_{i})} Without bounds on the complexity of the function space (formally, the reproducing kernel Hilbert space) available
Regularization_(mathematics)
NP-complete graph problem
from a computational complexity point of view. For example, the subgraph isomorphism problem is NP-complete on connected proper interval graphs and on
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Property of functions which is weaker than continuity
semicontinuous function is closed, such functions yield canonical stratifications of topological spaces into closed (thus Borel) pieces of increasing complexity. This
Semi-continuity
Creating sequence of numbers that cannot be predicted
for proper distributions). A second method called the acceptance-rejection method, involves choosing an x and y value and testing whether the function of
Random_number_generation
Set of rules defining correctly structured programs
This article contains APL source code. Without proper rendering support, you may see question marks, boxes, or other symbols instead of APL symbols. The
APL_syntax_and_symbols
Computer science concept
computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize
Polynomial_hierarchy
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
Target set of a mathematical function
part of a function f if f is defined as just a graph. For example, in set theory it is desirable to permit the domain of a function to be a proper class X
Codomain
Branch of mathematics
worst-case complexity, and the complexity bound of Lazard's algorithm of 1979 may frequently apply. Faugère F5 algorithm realizes this complexity, as it may
Algebraic_geometry
Size of a set in mathematics
place, it is called injective. If a function covers every member in the output set, it is called surjective. If a function is both injective and surjective
Cardinality
Self-balancing binary search tree data structure
hashcodes, a red–black tree is used. This results in the improvement of time complexity of searching such an element from O ( m ) {\displaystyle O(m)} to O (
Red–black_tree
Average uncertainty in variable's states
the books. The key idea is that the complexity of the probabilistic model must be considered. Kolmogorov complexity is a theoretical generalization of
Entropy_(information_theory)
Measure of similarity and diversity between sets
1-T_{s}} . This function is a proper distance metric. In application, Tanimoto distance can be harmfully confused with Jaccard distance as a proper distance
Jaccard_index
Form of second-order logic
second-order logic (ESO) captures precisely the descriptive complexity of the complexity class NP. By analogy, the class of problems that may be expressed
Monadic_second-order_logic
Mathematical model of computation
Simple examples are vending machines, which dispense products when the proper combination of coins is deposited; elevators, whose sequence of stops is
Finite-state_machine
Algorithm for linear programming
interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint. The simplicial cones in question
Simplex_algorithm
Concept in machine learning
convergence rates (with regards to sample complexity) than for the logistic loss or hinge loss functions. In addition, functions which yield high values of f ( x
Loss functions for classification
Loss_functions_for_classification
Resistance of a password to being guessed
average, to guess it correctly. The strength of a password is a function of length, complexity, and unpredictability. Using strong passwords lowers the overall
Password_strength
Subpermutation of a longer permutation
separable permutations. Later, Jelínek and Kynčl completely resolved the complexity of Av ( σ ) {\displaystyle {\mbox{Av}}(\sigma )} -Pattern PPM by showing
Permutation_pattern
Class of algorithms for pattern analysis
analyzed using statistical learning theory (for example, using Rademacher complexity). Kernel methods can be thought of as instance-based learners: rather
Kernel_method
Similarity measure for number sequences
the field of data mining. One advantage of cosine similarity is its low complexity, especially for sparse vectors: only the non-zero coordinates need to
Cosine_similarity
Use of functions that call themselves
(usually) then be simplified into a single Big-O term. If the time-complexity of the function is in the form T ( n ) = a ⋅ T ( n / b ) + f ( n ) {\displaystyle
Recursion_(computer_science)
Programming language
in advance. Therefore, the set of functions computable by LOOP-programs is a proper subset of computable functions (and thus a subset of the computable
LOOP_(programming_language)
Copy of a directed graph with redundant edges removed
subgraphs is minimal (by the proper subset definition): there is no transitive reduction. As Aho et al. show, when the time complexity of graph algorithms is
Transitive_reduction
Mapping of mathematical formulas to a particular meaning
discussed above. When the domain is a proper class, each function and relation symbol may also be represented by a proper class. In Bertrand Russell's Principia
Structure (mathematical logic)
Structure_(mathematical_logic)
Ordered listing of items in collection
if there exists an injective function from it into the natural numbers. The natural numbers are enumerable by the function f(x) = x. In this case f : N
Enumeration
Unicode character block
This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols. In Unicode, the Sumero-Akkadian
Cuneiform_(Unicode_block)
On finding a repeating loop in a sequence
is a proper factor of n, as desired. If n is not prime, it must have at least one factor p ≤ √n, and by the birthday paradox, a random function f has
Cycle_detection
Mathematical function on ordinals
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced
Veblen_function
studies was the elaboration of linguistic-philosophical notions whose complexity and subtlety has only recently come to be appreciated. Many of the most
Philosophy_of_language
Technique in mathematical modeling
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely
Model_order_reduction
Sorting algorithm
efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each element in the input is no more than k places away
Insertion_sort
Type of mathematical expression
computational complexity theory the phrase polynomial time means that the time it takes to complete an algorithm is bounded by a polynomial function of some
Polynomial
Book by Stephen Wolfram
applications is demonstrating how little complexity it takes to achieve interesting behavior, and how the proper methodology can discover this behavior
A_New_Kind_of_Science
Philosophical thought experiment
spontaneously form literally any structure of any degree of complexity, including a functioning human brain. The scenario initially involved only a single
Boltzmann_brain
Collection of mathematical objects
being provided by the function x ↦ tan ( π x / 2 ) {\displaystyle x\mapsto \tan(\pi x/2)} . Having the same cardinality of a proper subset is a characteristic
Set_(mathematics)
Combustion models of fuel reactions and energy release for computational fluid dynamics
above-mentioned applications. With the added complexity of chemical kinetics and achieving reacting flow mixture environment, proper modeling physics has to be incorporated
Combustion_models_for_CFD
complexity of matrix multiplication. 4. Written as a function of another function, it is used for comparing the asymptotic growth of two functions.
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Distribution estimation technique
1 , … , x n , {\displaystyle x_{1},\ldots ,x_{n},} different proper weighting functions can be employed (e.g., see ). In an adaptive setting, the proposal
Importance_sampling
Any web page served from a single domain
and interactivity (such as for a rich Web application that mirrors the complexity of a desktop application like a word processor). Examples of such plug-ins
Website
Standard system of axiomatic set theory
containing urelements (elements that are not themselves sets). Furthermore, proper classes (collections of mathematical objects defined by a property shared
Zermelo–Fraenkel_set_theory
Axiom in set theory
ZFC, as the choice function τ is a proper class and in ZFC one cannot quantify over classes. It can be stated by adding a new function symbol τ to the language
Axiom_of_global_choice
Programming paradigm based on applying and composing functions
are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that
Functional_programming
Decision-making framework
people's behaviour. The framework draws on research into systems theory, complexity theory, network theory and learning theories. The idea of the Cynefin
Cynefin_framework
Problem-solving technique and algorithmic paradigm
the curse of dimensionality. One example of a case where combinatorial complexity leads to solvability limit is in solving chess. Chess is not a solved
Brute-force_search
Putting data in the source code of a program
in Group Policy in Windows 2000 or above. The proper way to get it is to call the SHGetFolderPath function. An indirect reference, such as a variable inside
Hard_coding
Molar and premolar teeth in mammals
synapsids, although the diversity of therapsid molar patterns and the complexity in the molars of the earliest mammals make determining how this happened
Cheek_teeth
Mackie as a mechanism for understanding and controlling the computational complexity cost of beta reduction. In beta reduction, one defines the value of the
Director_string
Measure in risk analysis
the relative level of risk-reduction provided by a safety instrumented function (SIF), i.e. the measurement of the performance required of the SIF. In
Safety_integrity_level
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the
Bijection
Writing system of the ancient Near East
This article contains cuneiform script. Without proper rendering support, you may see question marks, boxes, or other symbols instead of cuneiform script
Cuneiform
Programming language family
fdefinition 'f to a new function object. fdefinition is a global function definition for the function named f. #' is an abbreviation for function special operator
Lisp_(programming_language)
Process of using data analysis for predicting population data from sample data
developed from ideas in information theory and the theory of Kolmogorov complexity. The (MDL) principle selects statistical models that maximally compress
Statistical_inference
Size of a possibly infinite set
{\displaystyle \mathbb {N} } is a proper subset of Q {\displaystyle \mathbb {Q} } —something that cannot happen with proper subsets of finite sets. However
Cardinal_number
Method of designing specialized integrated circuits
representations of the elemental NAND, NOR, and XOR Boolean function, although cells of much greater complexity are commonly used (such as a 2-bit full-adder, or
Standard_cell
Russell (1995), "A personal view of average-case complexity", Proc. Tenth Annual Structure in Complexity Theory Conference (SCT'95), pp. 134–147, CiteSeerX 10
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
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
Branch of mathematical logic
natural numbers definable by a formula of a given complexity exists. In this context, the complexity of formulas is measured using the arithmetical hierarchy
Reverse_mathematics
Enclosed structure
a house or factory. Buildings come in a variety of sizes, shapes, and functions, and have been adapted throughout history for numerous factors, from building
Building
Type of set in mathematics
viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved
K-trivial_set
Metric in computer science
with adjacent transpositions. Adding transpositions adds significant complexity. The difference between the two algorithms consists in that the optimal
Damerau–Levenshtein_distance
Proof in set theory
This leads to the family of functions: fb (t) = 0.tb. The functions f b(t) are injections, except for f 2(t). This function will be modified to produce
Cantor's_diagonal_argument
American Christian philosopher (born 1932)
true. Plantinga seeks to defend this view of proper function against alternative views of proper function proposed by other philosophers which he groups
Alvin_Plantinga
Programming language
ambiguity and because of its former domain name, golang.org, however, its proper name is Go. There are two major implementations: The original, self-hosting
Go_(programming_language)
Measure of heating or cooling used in agriculture
degree day is computed as the integral of a function of time that generally varies with temperature. The function is truncated to upper and lower limits that
Degree_day
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
Male
English
English name derived from Latin Prosperus, PROSPER means "fortunate, successful."
Girl/Female
American, Australian, British, Chinese, English
Flute Player; A Young Dove; Piper
Surname or Lastname
English
English : status name for a reeve, the chief magistrate or bailiff of a district, from Latin praetor.Dutch : occupational name for a warden of meadows or a gamekeeper, from Middle Dutch prater, preter (Latin pratarius, a derivative of pratum ‘meadow’).Dutch and North German : nickname for an excessively talkative person, from Middle Low German praten ‘to talk or prattle’.German : variant of Brater (see Brader 2).
Girl/Female
Latin
Prosper.
Boy/Male
English
Maker of rope.
Surname or Lastname
English
English : occupational name for a maker or seller of rope, from an agent derivative of Old English rÄp ‘rope’. See also Roop.Variant of French Robert.North German (Röper) : occupational name for a town crier, from an agent derivative of Middle Low German rÅpen ‘to call’.
Boy/Male
Australian, Christian, Danish, Finnish, French, German, Latin
Fortunate
Girl/Female
English American
Piper.
Male
English
English occupational surname transferred to unisex forename use, derived from Middle English pipere, PIPER means "pipe-player."
Male
Italian
Italian and Spanish form of Latin Prosperus, PROSPERO means "fortunate, successful." Shakespeare used this name in his play "The Tempest."
Surname or Lastname
English and Irish
English and Irish : occupational name for a maker and seller of woolen cloth, Anglo-Norman French draper (Old French drapier, an agent derivative of drap ‘cloth’). The surname was introduced to Ulster in the 17th century. Draperstown in County Londonderry was named for the London Company of Drapers, which was allocated the land in the early 17th century.
Boy/Male
English American
Grove dweller. Used as both surname and given name. Famous bearer: American president Grover...
Girl/Female
American, Australian, British, English
From the Pepper Plant; Hot Spice
Surname or Lastname
English and Scottish
English and Scottish : occupational name for the gatekeeper of a walled town or city, or the doorkeeper of a great house, castle, or monastery, from Middle English porter ‘doorkeeper’, ‘gatekeeper’ (Old French portier). The office often came with accommodation, lands, and other privileges for the bearer, and in some cases was hereditary, especially in the case of a royal castle. As an American surname, this has absorbed cognates and equivalents in other European languages, for example German Pförtner (see Fortner) and North German Poertner.English : occupational name for a man who carried loads for a living, especially one who used his own muscle power rather than a beast of burden or a wheeled vehicle. This sense is from Old French porteo(u)r (Late Latin portator, from portare ‘to carry or convey’).Dutch : occupational name from Middle Dutch portere ‘doorkeeper’. Compare 1.Dutch : status name for a freeman (burgher) of a seaport, Middle Dutch portere, modern Dutch poorter.Jewish (Ashkenazic) : adoption of the English or Dutch name in place of some Ashkenazic name of similar sound or meaning.
Boy/Male
British, Chinese, English
From the Pepper Plant
Girl/Female
Arabic, Muslim
Fair Complexion; Wife of the Prophet PBUH
Male
English
English occupational surname transferred to forename use, PORTER means "doorkeeper."
Surname or Lastname
English and North German
English and North German : from Middle English peper, piper, Middle Low German peper ‘pepper’, hence a metonymic occupational name for a spicer; alternatively, it may be a nickname for a small man (as if the size of a peppercorn) or one with a fiery temper, or for a dark-haired person (from the color of a peppercorn) or anecdotal for someone who paid a peppercorn rent.Americanized form of the Ashkenazic Jewish ornamental name Pfeffer, or Fef(f)er, a cognate, from Yiddish fefer ‘pepper’.Irish : variant of Peppard.
Male
Norwegian
Norwegian variant form of Scandinavian Frode, FRODER means "wise."
Surname or Lastname
French
French : from a Germanic personal name, Hrodmar, composed of hrÅd ‘renown’, ‘glory’ + mÄr ‘famous’.English : habitational name from Cromer in Norfolk, recorded in the 13th century as Crowemere, from Old English crÄwe ‘crow’ + mere ‘lake’.Variant spelling of German and Jewish Kromer.
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
Female
Chinese
fine, beautiful.
Boy/Male
Hindu, Indian
Pure
Girl/Female
Arabic
Fasting
Boy/Male
Indian
A name of Vishnu, Without enemies
Biblical
ruling; coming down
Girl/Female
Indian
Blessed
Girl/Female
Muslim
Her kuniyah was umm sulaym
Boy/Male
Australian, Bengali, Indian, Muslim
Star
Boy/Male
Arabic, Muslim
Slave of the One who is Light
Girl/Female
Australian, French, Polish
Weapon; Derived from Medieval Male Form of Matthew
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
PROPER COMPLEXITY-FUNCTION
a.
Pertaining to one of a species, but not common to the whole; not appellative; -- opposed to common; as, a proper name; Dublin is the proper name of a city.
v. t.
To gratify inordinately; to indulge to excess; as, to pamper pride; to pamper the imagination.
v. t.
To sprinkle or season with pepper.
n.
See Grouper.
adv.
Properly; hence, to a great degree; very; as, proper good.
pl.
of Complexity
n.
Any plant of the genus Capsicum, and its fruit; red pepper; as, the bell pepper.
adv.
In an appropriate or proper manner; fitly; properly.
n.
Work done by a cooper in making or repairing barrels, casks, etc.; the business of a cooper.
a.
Not proper or peculiar; improper.
n.
One who gropes; one who feels his way in the dark, or searches by feeling.
n.
The general appearance or aspect; as, the complexion of the sky; the complexion of the news.
n.
Complexity.
a.
Belonging to the natural or essential constitution; peculiar; not common; particular; as, every animal has his proper instincts and appetites.
n.
Same as Proleg.
n.
The state of being complex; complexity.
v. t.
To do the work of a cooper upon; as, to cooper a cask or barrel.
a.
Not proper; not suitable; not fitted to the circumstances, design, or end; unfit; not becoming; incongruous; inappropriate; indecent; as, an improper medicine; improper thought, behavior, language, dress.
a.
Rightly so called; strictly considered; as, Greece proper; the garden proper.
a.
Befitting one's nature, qualities, etc.; suitable in all respect; appropriate; right; fit; decent; as, water is the proper element for fish; a proper dress.