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Type of computational algorithm
computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means
Log-space_reduction
Type of computer science algorithm
the working space of the algorithm. In theoretical applications such as log-space reductions, it is more typical to always ignore output space (in these
In-place_algorithm
Class in computational complexity theory
under the unproven assumption that NC ≠ P. If we use the stronger log-space reduction, this remains true, but additionally we learn that all P-complete
P-complete
SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem
SL_(complexity)
Transformation of one computational problem to another
hierarchy, polynomial-time reductions are used. When studying classes within P such as NC and NL, log-space reductions are used. Reductions are also used in computability
Reduction_(complexity)
under a log-space reduction. This remains true for the stronger case of first-order reductions (Immerman 1999, p. 51). The log-space reduction from any
St-connectivity
complexity of decision problems. The term L reduction is sometimes used to refer to log-space reductions, by analogy with the complexity class L, but
L-reduction
Complexity class (logarithmic space)
way. Every non-trivial problem in L is complete under log-space reductions, so weaker reductions are required to identify meaningful notions of L-completeness
L_(complexity)
Marble-based mechanical toy computer
to run (encoded in unary), is complete under log-space reduction for CC, the class of problems log-space reducible to the stable marriage problem. He
Digi-Comp_II
Topics referred to by the same term
Large Space Telescope, the Hubble Space Telescope Living Systems Theory Log-space transducer, a type of Turing machine used for log-space reductions Löwenheim–Skolem
LST
Method for solving one problem using another
problem in P would be complete. Instead, weaker reductions such as log-space reductions or NC reductions are used for defining classes of complete problems
Polynomial-time_reduction
Inherent difficulty of computational problems
complexity of reductions, such as polynomial-time reductions or log-space reductions. The most commonly used reduction is a polynomial-time reduction. This means
Computational complexity theory
Computational_complexity_theory
Type of Turing reduction
projections where each subsequent reduction notion is weaker than the prior; see polynomial-time reduction and log-space reduction for details. Given decision
Many-one_reduction
Concept in computability theory
reduction of A {\displaystyle A} to B {\displaystyle B} that runs in polynomial time. The concept of log-space reduction is similar. These reductions
Turing_reduction
Complexity class
NP-complete under log space reductions. All currently known NP-complete problems remain NP-complete even under much weaker reductions such as A C 0 {\displaystyle
NP-completeness
Measure of the tendency of a substance to gain or lose electrons
Redox potential (also known as oxidation / reduction potential, ORP, pe, E r e d {\displaystyle E_{red}} , or E h {\displaystyle E_{h}} ) is a measure
Reduction_potential
American computer scientist
theory of computation, he was among the pioneers of the study of Log-space reductions and P-completeness. Neil D. Jones was a Knight of the Order of the
Neil_D._Jones
Set of problems in computational complexity theory
based on resource bounds, such as polynomial-time reductions and log-space reductions. Reductions motivate the concept of a problem being hard for a
Complexity_class
Computer science concept
In computer science, the reduction operator is a type of operator that is commonly used in parallel programming to reduce the elements of an array into
Reduction_operator
Chemical reaction with oxidation state changes
Redox (/ˈrɛdɒks/ RED-oks, /ˈriːdɒks/ REE-doks, reduction–oxidation or oxidation–reduction) is a type of chemical reaction in which the oxidation states
Redox
Complexity class
then defined as the class of all problems with an L-reduction (linear reduction, not log-space reduction) to problems in MaxSNP0. For example, MAX-3SAT is
SNP_(complexity)
define implicit transduction by the standard trick, also used in Log-space reduction. A function f : 2 ∗ → 2 ∗ {\displaystyle f:2^{*}\to 2^{*}} is implicitly
DLOGTIME
Password cracking dataset
decreasing this space requirement. The idea is to define a reduction function R that maps hash values back into values in P. The reduction function is, however
Rainbow_table
Simplifying data to facilitate analysis
specific criteria. Another example would be a log-linear model, obtaining a value at a point in m-D space as the product on appropriate marginal subspaces
Data_reduction
Function related to statistics and probability theory
with: log L ( α , β ∣ x ) = α log β − log Γ ( α ) + ( α − 1 ) log x − β x . {\displaystyle \log {\mathcal {L}}(\alpha ,\beta \mid x)=\alpha \log \beta
Likelihood_function
Measure of algorithmic complexity
( log a + log b ) {\displaystyle O(\log a+\log b)} arithmetic operations on numbers with at most O ( log a + log b ) {\displaystyle O(\log a+\log
Strongly-polynomial_time
otherwise specified, the reductions in this definition are assumed to be many-one reductions by a deterministic logarithmic-space algorithm. If an NL-complete
NL-complete
Data structure
}=b^{h}-1} The space required to store the tree is O ( n ) {\displaystyle O(n)} Inserting a record requires O ( log b n ) {\displaystyle O(\log _{b}n)} operations
B+_tree
Average uncertainty in variable's states
is H ( X ) := − ∑ x ∈ X p ( x ) log p ( x ) , {\displaystyle \mathrm {H} (X):=-\sum _{x\in {\mathcal {X}}}p(x)\log p(x),} where Σ {\displaystyle \Sigma
Entropy_(information_theory)
Optimization problem in computer science
deterministic polynomial-time reductions even when approximation within a factor 2 ( log n ) 1 − ε {\displaystyle 2^{(\log n)^{1-\varepsilon }}} is permitted
Lattice_problem
Optimal data structure for priority queues
of Ω ( log log n ) , {\displaystyle \Omega (\log \log n),} upper bound of O ( 2 2 log log n ) . {\displaystyle O(2^{2{\sqrt {\log \log n}}}).}
Strict_Fibonacci_heap
Computer security technique
2012-04-14 at the Wayback Machine Address Space Layout Randomization in Windows Vista - Michael Howard's Web Log ASLR for Windows 2000/XP/2003 (WehnTrust)
Address space layout randomization
Address_space_layout_randomization
Tree node with two other nodes as descendants
{n \over b})} space. Because b = 1 2 log n {\displaystyle b={1 \over 2}\log n} , O ( n b log n b ) {\displaystyle O({n \over b}\log {n \over b})}
Lowest_common_ancestor
provide a more flexible space-frequency signal decomposition several filters (including wavelets) have been proposed. The Log-Gabor filter is one such
Log_Gabor_filter
Statistical theorem
In statistics, Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals
Wilks'_theorem
Signal attenuation in telecommunications
path attenuation, is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is a major component
Path_loss
Technique for dimensionality reduction
nonlinear dimensionality reduction technique for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions
T-distributed stochastic neighbor embedding
T-distributed_stochastic_neighbor_embedding
Method of estimating the parameters of a statistical model, given observations
θ0. Compactness: the parameter space Θ of the model is compact. The identification condition establishes that the log-likelihood has a unique global maximum
Maximum_likelihood_estimation
Complexity class of approximable problems
Log-APX-completeness and poly-APX-completeness are defined in terms of AP-reductions rather than PTAS-reductions; this is because PTAS-reductions are
APX
Complexity class of decision problems
algorithm whose space complexity is bounded by a polylogarithmic function in the size of the input. In other words, polyL = DSPACE((log n)O(1)), where
PolyL
Variable representing a random phenomenon
) ) . {\displaystyle F_{Y}(y)=P(Y\leq y)=P(\mathrm {log} (1+e^{-X})\leq y)=P(X\geq -\mathrm {log} (e^{y}-1)).\,} The last expression can be calculated
Random_variable
Computational geometry problem
the somewhat slower O ( n log n ) {\displaystyle O(n\log n)} time bound, and this is optimal for this model, by a reduction from the element uniqueness
Closest pair of points problem
Closest_pair_of_points_problem
American actress (born 1998)
She is a purple belt in taekwondo. In 2015, Winter underwent breast reduction surgery. In a 2016 interview with Nightline, Winter explained the awkwardness
Ariel_Winter
n log n ) {\displaystyle O(n\log n)} space, query time O ( log n ) {\displaystyle O(\log n)} , and stretch O ( log n ) {\displaystyle O(\log n)}
Distance_oracle
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
( log ( p ( n ) ) p ( n ) 3 ) {\displaystyle O(\log(p(n))p(n)^{3})} . Thus the transformation is certainly a polynomial-time many-one reduction, as
Cook–Levin_theorem
Computational task of sorting whole numbers
sorting algorithm, it is possible to sort in time O(n log log n); however, the range reduction part of this algorithm requires either a large memory (proportional
Integer_sorting
Message encoded with more bits than needed
maximum possible value log ( | A X | ) {\displaystyle \log(|{\mathcal {A}}_{X}|)} . Informally, it is the amount of wasted "space" used to transmit certain
Redundancy (information theory)
Redundancy_(information_theory)
Computational problem
(Author's draft) Richard E. Ladner (Jan 1975). "The circuit value problem is log space complete for P". ACM SIGACT News. 7 (101): 18–20. doi:10.1145/990518.990519
Circuit_value_problem
Neil Armstrong's words on landing on the Moon
Language Log. June 20, 2016. Retrieved June 7, 2026. Nickell, Duane S. (2008). Guidebook for the Scientific Traveler: Visiting Astronomy and Space. New Brunswick
One_small_step
Minus Space is an art gallery located in Dumbo, Brooklyn, NY. It specializes in abstract art and reductive art. Minus Space began as an online curatorial
Minus_Space
Search tree data structure
S2CID 12943246. Willar, Dan E. (27 January 1983). "Log-logarithmic worst-case range queries are possible in space O(n)". Information Processing Letters. 17 (2):
Trie
Method of detecting shapes within images
log-likelihood on the shape space. The linear Hough transform algorithm estimates the two parameters that define a straight line. The transform space
Hough_transform
American budget reconciliation law
The Inflation Reduction Act of 2022 (IRA), Pub. L. 117–169 (text) (PDF), is a United States federal law which aimed to reduce the federal government budget
Inflation_Reduction_Act
more space, subject to certain conditions. For example, a deterministic Turing machine can solve more decision problems in space n log n than in space n
Structural_complexity_theory
proved an upper bound of O d ( ( log n ) d + 1 / 2 log log n ) {\displaystyle O_{d}((\log n)^{d+1/2}{\sqrt {\log \log n}})} with a simple proof. When
Geometric_discrepancy
Class of statistical models
log(μ) be a linear model. This produces the "cloglog" transformation log ( − log ( 1 − p ) ) = log ( μ ) . {\displaystyle \log(-\log(1-p))=\log(\mu
Generalized_linear_model
Method in natural language processing
Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, explainable knowledge
Word_embedding
Estimate of the importance of a word in a document
= − log P ( t | D ) = log 1 P ( t | D ) = log N | { d ∈ D : t ∈ d } | {\displaystyle {\begin{aligned}\mathrm {idf} &=-\log P(t|D)\\&=\log {\frac
Tf–idf
Upper limit on entropy in physics
= − t r ( ρ V log ρ V ) + t r ( ρ V 0 log ρ V 0 ) {\displaystyle S_{V}=S(\rho _{V})-S(\rho _{V}^{0})=-\mathrm {tr} (\rho _{V}\log \rho _{V})+\mathrm
Bekenstein_bound
Algorithmic technique using hashing
guarantees: space: O ( n 1 + ρ P 1 − 1 d log 2 n ) {\displaystyle O(n^{1+\rho }P_{1}^{-1}d\log ^{2}n)} ; query time: O ( n ρ P 1 − 1 ( k t + d ) log n )
Locality-sensitive_hashing
Family of probability distributions related to the normal distribution
called the natural parameter space. It can be shown that the natural parameter space is always convex. A(η) is called the log-partition function because
Exponential_family
functional is an analogy of the log-norm functional of the moment map in geometric invariant theory and symplectic reduction. The Mabuchi functional appears
Mabuchi_functional
Office organization system
own personal desk. A primary motivation for hot-desking is cost reduction through space savings—up to 30% in some cases. Hot desking is especially valuable
Hot_desking
waste linear (Ω(n)) space, where n is the number of elements in the array, hashed array trees waste only order O(√n) storage space. An optimization of
Hashed_array_tree
Algorithm to multiply two numbers
log n log log n ) {\displaystyle O(n\log n\log \log n)} . In 2007, Martin Fürer proposed an algorithm with complexity O ( n log n 2 Θ ( log ∗
Multiplication_algorithm
Mathematical result
low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension
Johnson–Lindenstrauss_lemma
Optimization problem in computer science
this space, the nearest neighbour of every point can be found in O(n log n) time and the m nearest neighbours of every point can be found in O(mn log n)
Nearest_neighbor_search
Branch of physical chemistry
follows: E c e l l ∘ = 0.05916 V n log K {\displaystyle E_{cell}^{\circ }={\frac {0.05916\,\mathrm {V} }{n}}\log K} The standard potential of an electrochemical
Electrochemistry
Unbiased statistical estimator minimizing variance
− x exp ( − θ log ( 1 + e − x ) + log ( θ ) ) {\displaystyle {\frac {e^{-x}}{1+e^{-x}}}\exp \left(-\theta \log(1+e^{-x})+\log(\theta )\right)}
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Experiment methodology
cleaning Outlier Winsorizing Truncation Missing data Data reduction Dimensionality reduction Principal component analysis Factor analysis Time-series preprocessing
A/B_testing
Mathematical game
O(n/log n) pebbles where the constant depends on the maximum in-degree. This enabled them to prove that DTIME(f(n)) is contained in DSPACE(f(n)/log f(n))
Pebble_game
Discrete Fourier transform algorithm
arises if one simply applies the definition of DFT, to O ( n log n ) {\textstyle O(n\log n)} , where n is the length of the sequence. The difference
Fast_Fourier_transform
Abstract data type in computer science
predecessor and successor] operations in O ( log log C ) {\displaystyle O(\log \log C)} time, but has a space cost for small queues of about O ( 2 m /
Priority_queue
Distribution of an uncertain quantity
over a probability space it equals one. Hence we can write the asymptotic form of KL as K L = − log ( 1 k I ( x ∗ ) ) − ∫ p ( x ) log [ p ( x ) ] d x
Prior_probability
Concept in machine learning
= 1 log ( 2 ) [ − e v 1 + e v log e v 1 + e v − ( 1 − e v 1 + e v ) log ( 1 − e v 1 + e v ) ] + ( 1 − e v 1 + e v ) [ − 1 log ( 2 ) log ( e
Loss functions for classification
Loss_functions_for_classification
Mathematical operation in calculus
we have ( log u v ) ′ = ( log u + log v ) ′ = ( log u ) ′ + ( log v ) ′ . {\displaystyle (\log uv)'=(\log u+\log v)'=(\log u)'+(\log v)'.} So
Logarithmic_derivative
American computer scientist (born 1946)
version achieving O(log △ 1 + ϵ {\displaystyle \vartriangle ^{1+\epsilon }} ), as well as demonstrating a theoretical lower-bound of O(log △ {\displaystyle
Richard_Lipton
SpaceX family of liquid-fuel rocket engines
high area ratio, deep space Raptor engines. ... 'The engine thrust dropped roughly in proportion to the vehicle mass reduction from the first IAC talk
SpaceX_Raptor
Machine learning algorithm
_{i=1}^{J}-\Pr(i\mid a)\log _{2}\Pr(i\mid a)} That is, the expected information gain is the mutual information, meaning that on average, the reduction in the entropy
Decision_tree_learning
Statistical model for a binary dependent variable
a logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent variables
Logistic_regression
Concept of permanent human habitation outside of Earth
13/13". Log In ‹ Blogs @ Columbia Law School. Retrieved 15 October 2022. O'Neill, Gerard K. (1977). The High Frontier: Human Colonies in Space. Anchor
Space_colonization
Model for generating observable data in probability and statistics
cleaning Outlier Winsorizing Truncation Missing data Data reduction Dimensionality reduction Principal component analysis Factor analysis Time-series preprocessing
Generative_model
Class in computational complexity theory
restricted to at most two options at each step with O(log n) space and ( log n ) O ( 1 ) {\displaystyle (\log n)^{O(1)}} alternations. It is a major open question
NC_(complexity)
Concept in probability and statistics
_{\theta }\log(l(\theta ))} where log ( l ( θ ) ) = log ( P ( x 1 | θ ) ) + log ( P ( x 2 | θ ) ) + log ( P ( x 3 | θ ) ) + . . . + log ( P ( x
Independent and identically distributed random variables
Independent_and_identically_distributed_random_variables
Technique used in stochastic gradient variational inference
probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under
Reparameterization_trick
Mathematical and computational problem
most O P T + O ( log ( O P T ) ⋅ log log ( O P T ) ) {\displaystyle \mathrm {OPT} +{\mathcal {O}}(\log(\mathrm {OPT} )\cdot \log \log(\mathrm {OPT}
Bin_packing_problem
Numerical measure of a statistical relationship between variables
cleaning Outlier Winsorizing Truncation Missing data Data reduction Dimensionality reduction Principal component analysis Factor analysis Time-series preprocessing
Correlation_coefficient
Fractal composed of triangles
connected curve. Its Hausdorff dimension is log 4 log 2 = 2 {\textstyle {\tfrac {\log 4}{\log 2}}=2} ; here "log" denotes the natural logarithm, the numerator
Sierpiński_triangle
Problem in computational complexity theory
algorithm that solves 3SUM in O ( n 2 / ( log n / log log n ) 2 / 3 ) {\displaystyle O(n^{2}/({\log n}/{\log \log n})^{2/3})} time. Additionally, Grønlund
3SUM
a 30% reduction in the industry's work force. 300,000 people worked in the industry at the end of 1994, down from 400,000 in 1987, and the space program's
Space_industry_of_Russia
Maximal subgraph whose vertices can reach each other
log 2 n / log log n ) {\displaystyle O(\log ^{2}n/\log \log n)} per change and time O ( log n / log log n ) {\displaystyle O(\log n/\log \log
Component_(graph_theory)
Belgian mathematician (1954–2018)
metric dimension reduction, which states that every metric space can be embedded into an l p {\displaystyle l_{p}} space of dimension O ( log 2 ( n ) ) {\displaystyle
Jean_Bourgain
Measure of dependence between two variables
1 2 log ( 2 π e σ i 2 ) = 1 2 + 1 2 log ( 2 π ) + log ( σ i ) , i ∈ { 1 , 2 } H ( X 1 , X 2 ) = 1 2 log [ ( 2 π e ) 2 | Σ | ] = 1 + log ( 2
Mutual_information
Type of machine learning model
log ( Pr ( correct token ) ) {\displaystyle y={\text{average }}\log(\Pr({\text{correct token}}))} , then the ( log x , y ) {\displaystyle (\log x
Large_language_model
Statistical evaluation method
point and the blue dashed maximum line that bounds the left side of the TOC space. The number of correct rejections at each threshold is the distance between
Total operating characteristic
Total_operating_characteristic
Experimental design framework
log ( p ( θ ∣ y , ξ ) ) p ( θ , y ∣ ξ ) d θ d y − ∫ log ( p ( θ ) ) p ( θ ) d θ = ∫ ∫ log ( p ( y ∣ θ , ξ ) ) p ( θ , y ∣ ξ ) d y d θ − ∫ log
Bayesian_experimental_design
Machine learning paradigm
more general strategy of dimensionality reduction, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning
Supervised_learning
Fast approximate median algorithm
yielding an optimal algorithm, with worst-case complexity O ( n log n ) {\displaystyle O(n\log n)} .[citation needed] The median of medians algorithm guarantees
Median_of_medians
President of the United States from 2021 to 2025
into the Inflation Reduction Act of 2022, covering deficit reduction, climate change, healthcare, and tax reform. The Inflation Reduction Act of 2022 was
Joe_Biden
Iterative method for finding maximum likelihood estimates in statistical models
expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a
Expectation–maximization algorithm
Expectation–maximization_algorithm
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