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Special-purpose computer
A graph reduction machine is a special-purpose computer built to perform combinator calculations by graph reduction. Examples include the SKIM ("S-K-I
Graph_reduction_machine
Efficient version of non-strict evaluation
In computer science, graph reduction implements an efficient version of non-strict evaluation, an evaluation strategy where the arguments to a function
Graph_reduction
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Swedish computer scientist
languages had been implemented via interpreted graph reduction. LML compiled to graph reduction machine (G-machine) code. Part of the development team at Epic
Lennart_Augustsson
Type of knowledge base
machine learning, particularly in graph neural networks, representation learning, and machine learning, have broadened the scope of knowledge graphs beyond
Knowledge_graph
Logical formalism using combinators instead of variables
Categorical abstract machine Combinatory categorial grammar Explicit substitution Fixed point combinator Graph reduction machine Lambda calculus and Cylindric
Combinatory_logic
Heuristic test for graph isomorphism
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
British academic and author
parallel machine design, the ALICE functional graph reduction machine (1985), a forerunner of the commercial ICL Goldrush parallel database machine (1992);
John_Darlington
Representation learning technique
Word2Vec), image embeddings for visual data, and knowledge graph embeddings for knowledge graphs, each tailored to tasks like NLP, computer vision, or recommendation
Embedding_(machine_learning)
Projection of data onto lower-dimensional manifolds
dimensionality reduction, such as singular value decomposition and principal component analysis. High dimensional data can be hard for machines to work with
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Overview of and topical guide to machine learning
Low-density separation Graph-based methods Co-training Transduction Deep learning Deep belief networks Deep Boltzmann machines Deep Convolutional neural
Outline_of_machine_learning
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Subset of artificial intelligence
detection Investment management Knowledge graph embedding Linguistics Machine learning control Machine perception Machine translation Material Engineering Marketing
Machine_learning
Dimensionality reduction of graph-based semantic data objects [machine learning task]
learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of
Knowledge_graph_embedding
combinator SKI combinator calculus B, C, K, W system SECD machine Graph reduction machine Sequent, sequent calculus Natural deduction Intuitionistic
List of functional programming topics
List_of_functional_programming_topics
Complexity class
problem Dominating set problem Graph coloring problem Sudoku To the right is a diagram of some of the problems and the reductions typically used to prove their
NP-completeness
Maximal subgraph whose vertices can reach each other
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph
Component_(graph_theory)
Mathematical proof about the permanent of matrices
equivalent matrix whose entries are all powers of 2. The reduction can be expressed in terms of graphs equivalent to the matrices. Let G {\displaystyle G}
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
Directed graph representing dependencies
the dependency graph is a graph G = ( S , T ) {\displaystyle G=(S,T)} with T ⊆ R {\displaystyle T\subseteq R} the transitive reduction of R. For example
Dependency_graph
Inherent difficulty of computational problems
is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected or not. The formal language associated
Computational complexity theory
Computational_complexity_theory
Unsolved problem in computational complexity theory
of problems with a polynomial-time Turing reduction to the graph isomorphism problem. If in fact the graph isomorphism problem is solvable in polynomial
Graph_isomorphism_problem
Process of reducing the number of random variables under consideration
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the
Dimensionality_reduction
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Open-source data analytics cluster computing framework
Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit
Apache_Spark
Type of computational problem
polynomial-time many-one counting reduction. This problem is equivalent to counting perfect matchings in a bipartite graph. Deciding whether perfect matchings
Counting_problem_(complexity)
American inventor and businessman
his early developments of graphical-numerical computing devices, data-reduction tools, and plotters. He was awarded America's National Medal of Technology
Joseph_Gerber
accepting computation paths is odd. An example of a ⊕P problem is "does a given graph have an odd number of perfect matchings?" The class was defined by Papadimitriou
Parity_P
t in a directed graph, if t is reachable from s. Formally, the decision problem is given by PATH = {⟨D, s, t⟩ | D is a directed graph with a path from
St-connectivity
the problem of determining whether, given a directed graph G and two nodes s and t on that graph, there is a path from s to t. ST-connectivity can be
NL-complete
Complexity class
machine. The problem is #P-hard, meaning that every other problem in #P has a polynomial-time Turing reduction or polynomial-time counting reduction to
♯P-complete
Graph data structure
In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Let Σ {\displaystyle \Sigma } be
E-graph
Node ordering for directed acyclic graphs
computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u
Topological_sorting
Combinatorial reconfiguration problem
max-degree 3 graphs. The reduction follows from QSAT and is outlined below. The above problem is PSPACE-Complete even if the constraint graph is planar,
Nondeterministic constraint logic
Nondeterministic_constraint_logic
Mathematical model of computation
given to the machine) and the outputs resulting from each input: The turnstile state machine can also be represented by a directed graph called a state
Finite-state_machine
Concept in machine learning
higher-level designs of machine learning in the form of tensor graphs. This leads to new architectures, such as tensor-graph convolutional networks (TGCN)
Tensor_(machine_learning)
Problem in theoretical computer science
many-one reduction shows that subgraph isomorphism is also NP-complete. An alternative reduction from the Hamiltonian cycle problem translates a graph G which
Subgraph_isomorphism_problem
Optimization algorithm
gradient descent Linear classifier Online machine learning Stochastic hill climbing Stochastic variance reduction ⊙ {\displaystyle \odot } denotes the element-wise
Stochastic_gradient_descent
Complexity class
Longest simple path Graph coloring; an application: register allocation in compilers Lists of problems Lists of unsolved problems Reduction (complexity) Unknowability
NP-hardness
Type of solar radiation modification
and North America since the 1980s, and more recently in China. These reductions have improved air quality but diminish the cooling influence of aerosols
Stratospheric aerosol injection
Stratospheric_aerosol_injection
Data structure representing a finite set of strings
Word Graph or DAWG" – JohnPaul Adamovsky teaches how to construct a DAFSA using an array of integers (Archived 22 July 2022 at the Wayback Machine) "Caroline
Deterministic acyclic finite state automaton
Deterministic_acyclic_finite_state_automaton
Measurable property or characteristic
tasks. Features are usually numeric, but other types such as strings and graphs are used in syntactic pattern recognition, after some pre-processing step
Feature_(machine_learning)
Classification of computer architectures
this, programs are represented as graphs of expressions, which are dynamically updated as reduction proceeds. Graph nodes may represent values, operations
Duncan's_taxonomy
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Class of artificial neural network
implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two
Restricted_Boltzmann_machine
Clustering methods
the graph. They also look at two approximation algorithms in the same paper. Spectral clustering has a long history. Spectral clustering as a machine learning
Spectral_clustering
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
Functional programming language
library. Computing is based on graph rewriting and reduction. Constants such as numbers are graphs and functions are graph rewriting formulas. This, combined
Clean_(programming_language)
Machine learning technique
Xiaolong (2018). Non-Local Neural Networks. CVPR. Veličković, Petar (2018). Graph Attention Networks. ICLR. Kitaev, Nikita (2020). Reformer: The Efficient
Attention_(machine_learning)
British-Canadian codebreaker and mathematician (1917–2002)
fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable importance. At a time when graph theory
W._T._Tutte
Type of database that uses vectors to represent other data
analyzing data with many aspects ("dimensions") Graph database – Database using graph structures for queries Machine learning – Subset of artificial intelligence
Vector_database
Complexity class of approximable problems
independent set in bounded-degree graphs (here, the approximation ratio depends on the maximum degree of the graph, but is constant if the max degree
APX
Probabilistic model
statistics—particularly Bayesian statistics—and machine learning. Generally, probabilistic graphical models use a graph-based representation as the foundation
Graphical_model
Unsolved problem in computer science
about Turing machines as they relate to the definition of NP. However, after this problem was proved to be NP-complete, proof by reduction provided a simpler
P_versus_NP_problem
Algorithm for modelling sequential data
level. seq2seq – Family of machine learning approaches Circuit (neural network) – Interpretable computational sub-graphs within artificial neural networks
Transformer_(deep_learning)
Technique for dimensionality reduction
proposed the t-distributed variant. It is a nonlinear dimensionality reduction technique for embedding high-dimensional data for visualization in a low-dimensional
T-distributed stochastic neighbor embedding
T-distributed_stochastic_neighbor_embedding
Artificial intelligence algorithm
Tsetlin machine composites: plug-and-play collaboration between specialized Tsetlin machines Contracting Tsetlin machine with absorbing automata Graph Tsetlin
Tsetlin_machine
Research field in deep learning
Marc; Kwitt, Roland (2020-11-21). "Graph Filtration Learning". Proceedings of the 37th International Conference on Machine Learning. PMLR: 4314–4323. arXiv:1905
Topological_deep_learning
edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These
Multimodal representation learning
Multimodal_representation_learning
Mathematical-logic system based on functions
graphs extended with letrec, to detect possibly infinite unwinding trees; 2) the representational calculus with β-reduction of scoped lambda graphs constitute
Lambda_calculus
Set of methods for supervised statistical learning
the most votes determines the instance classification. Directed acyclic graph SVM (DAGSVM) Error-correcting output codes Crammer and Singer proposed a
Support_vector_machine
Machine-learning process
that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. Grammatical inference
Grammar_induction
Property of a model
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions
Bias–variance_tradeoff
Measures to reduce poverty permanently
Poverty reduction, poverty relief, or poverty alleviation is a set of measures, both economic and humanitarian, that are intended to permanently lift
Poverty_reduction
Type of Turing reduction
and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances of one decision problem
Many-one_reduction
Plotting by a computer application
finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify
Pathfinding
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Algorithmic complexity class
Turing machine. A decision problem is EXPTIME-complete if it is in EXPTIME and every problem in EXPTIME has a polynomial-time many-one reduction to it
EXPTIME
Set of learning techniques in machine learning
machines (RBMs) are often used as a building block for multilayer learning architectures. An RBM can be represented by an undirected bipartite graph consisting
Feature_learning
Optimization algorithm
f {\displaystyle f} is assumed to be defined on the plane, and that its graph has a bowl shape. The blue curves are the contour lines, that is, the regions
Gradient_descent
Standard representation of a mathematical object
normal form. In graph theory, a branch of mathematics, graph canonization is the problem of finding a canonical form of a given graph G. A canonical form
Canonical_form
Political-economic model common across Europe
following: Reduction in poverty. Protection against labour market risks. Rewards for labour participation. The graph on the right shows the reduction in inequality
European_social_model
Computational problem in graph theory
minimum-weight closure in a vertex-weighted directed graph. It may be solved in polynomial time using a reduction to the maximum flow problem. It may be used to
Closure_problem
determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices
SL_(complexity)
Electronics soldering process
appliances). There are many types of wave solder machines; however, the basic components and principles of these machines are the same. The basic equipment used
Wave_soldering
Task of computing complete subgraphs
vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what
Clique_problem
Class of algorithms for pattern analysis
data, graphs, text, images, as well as vectors. Algorithms capable of operating with kernels include the kernel perceptron, support-vector machines (SVM)
Kernel_method
Directed graph describing citations in documents
A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection
Citation_graph
Relation specifying a rewrite for each object, compatible with a reduction relation
Sorbonne Paris Cité. p. 62. Partain, William D. (December 1989). Graph Reduction Without Pointers (PDF) (PhD). University of North Carolina at Chapel
Reduction_strategy
Cycles in a graph that cover each edge twice
the set S, so the reductions in S are not strong enough to rule out the possibility that G might be a minimal counterexample. If a graph has a cycle double
Cycle_double_cover
Independent set which is not a subset of any other independent set
In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. In other
Maximal_independent_set
Device used for calculations
calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher-dimensional
Calculator
tree problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific types (triangles
List_of_NP-complete_problems
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Research field that lies at the intersection of machine learning and computer security
Adversarial machine learning is the study of the attacks on machine learning algorithms, and of the defenses against such attacks. Machine learning techniques
Adversarial_machine_learning
Category of formal programming language semantics
are given as a set of reduction rules that each specify a single potential reduction step. For example, the following reduction rule states that an assignment
Operational_semantics
discontinuity is shown within the red circle in graph 4. It is the reason the strip is given a light reduction (~1.3%) normally referred to as an elongation
Tandem_rolling_mill
Place in Abyei Area
Abyei Area through Good Governance and Poverty Reduction" Archived July 24, 2011, at the Wayback Machine Retrieved 24 July 2009. Aafriquejet; 01.19.2011
Abyei_(town)
Class of problems in computer science
maximum independent set in an interval graph. A generalization of the problem considers k > 1 {\displaystyle k>1} machines/resources. Here the goal is to find
Interval_scheduling
Variant of the traveling salesman problem
Hamiltonian cycle in a graph G with no edge longer than x?", is NP-complete. NP-completeness follows immediately by a reduction from the problem of finding
Bottleneck traveling salesman problem
Bottleneck_traveling_salesman_problem
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Graphical model of computation
calculus, such as efficient closed reduction and optimal, in Lévy's sense, Lambdascope. Interactions nets are graph-like structures consisting of agents
Interaction_nets
Machine learning strategy
strategies: Learning is accomplished by applying dimensionality reduction to graphs and figures like scatter plots. Then the user is asked to label the
Active learning (machine learning)
Active_learning_(machine_learning)
British computer scientist (1946–2023)
first for functional programming based on lazy evaluation, combinator graph reduction, and polymorphic types: SASL (1972), Kent Recursive Calculator (KRC)
David Turner (computer scientist)
David_Turner_(computer_scientist)
Class in computational complexity theory
is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis
P-complete
Branch of computational complexity theory
include deciding if a given graph contains a dominating set of size k. deciding if a given nondeterministic multi-tape Turing machine accepts within k steps
Parameterized_complexity
American computer scientist
Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning. IEEE Trans. Vis. Comput. Graph. 26(1): 45-55 (2020) Jianping Kelvin
Kwan-Liu_Ma
Field of electrical engineering
graph. Graph signal processing presents several key points such as sampling signal techniques, recovery techniques and time-varying techiques. Graph signal
Signal_processing
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
Girl/Female
Tamil
Education
Boy/Male
Arabic, Muslim
Education
Boy/Male
Arabic, Modern
Grape
Girl/Female
Muslim
Grape vine
Boy/Male
Muslim
Grape
Girl/Female
Indian, Marathi
Education
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Indian
Education
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Tamil
Education
Girl/Female
Hindu, Indian, Tamil
Education
Girl/Female
Muslim
Grape like
Girl/Female
Hindu
Education
Girl/Female
Indian
Grape like
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Tamil
Education
Boy/Male
Indian
Grape
Girl/Female
Indian
Education
Girl/Female
Indian
Grape vine
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
Boy/Male
Indian, Punjabi, Sikh
God as Protector
Girl/Female
American, Australian, British, Christian, English, French, German, Greek, Irish, Swedish
Pure; Clear; Courage; Purity; Yeats; Countess; Devil
Boy/Male
Indian, Tamil
Excellent Pearl
Boy/Male
Muslim
Obedient, Willing
Boy/Male
Indian
Faith; Trust
Boy/Male
Gaelic
From the head of the cliff.
Girl/Female
American, British, English, French, Latin
Majestic; Variant of Augustine; Worthy of Respect
Female
English
Slovene form of English Margaret, MARJETA means "pearl."
Girl/Female
Tamil
Abhimatha | அபீமதா
Desired
Girl/Female
Indian, Tamil
Wisdom; Star
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
GRAPH REDUCTION-MACHINE
n.
The wrongful, and usually the forcible, carrying off of a human being; as, the abduction of a child, the abduction of an heiress.
n.
A process of demonstration in which a general truth is gathered from an examination of particular cases, one of which is known to be true, the examination being so conducted that each case is made to depend on the preceding one; -- called also successive induction.
n.
A reductive agent.
v. t.
The bringing of a syllogism in one of the so-called imperfect modes into a mode in the first figure.
n.
The act or process of inferring by deduction or induction.
v. t.
The process of making a copy of something, as a figure, design, or draught, on a smaller scale, preserving the proper proportions.
n.
That which is deducted; the part taken away; abatement; as, a deduction from the yearly rent.
n.
The amount abated; that which is taken away by way of reduction; deduction; decrease; a rebate or discount allowed.
v. t.
The act, process, or result of reducing; as, the reduction of iron from its ores; the reduction of aldehyde from alcohol.
n.
The mutual or reciprocal action of chemical agents upon each other, or the action upon such chemical agents of some form of energy, as heat, light, or electricity, resulting in a chemical change in one or more of these agents, with the production of new compounds or the manifestation of distinctive characters. See Blowpipe reaction, Flame reaction, under Blowpipe, and Flame.
n.
Act of deducting or taking away; subtraction; as, the deduction of the subtrahend from the minuend.
n.
The action by which the parts of the body are drawn towards its axis]; -- opposed to abduction.
v. t.
The operation of restoring a dislocated or fractured part to its former place.
n.
The act of reducing, or state of being reduced; conversion to a given state or condition; diminution; conquest; as, the reduction of a body to powder; the reduction of things to order; the reduction of the expenses of government; the reduction of a rebellious province.
n.
The act or process of educating; the result of educating, as determined by the knowledge skill, or discipline of character, acquired; also, the act or process of training by a prescribed or customary course of study or discipline; as, an education for the bar or the pulpit; he has finished his education.
n.
Reduction.
n.
That which seduces, or is adapted to seduce; means of leading astray; as, the seductions of wealth.
n.
A red crystalline nitrogenous substance or artificial production, which by reduction passes directly to indigo.
n.
The act or process or producing, bringing forth, or exhibiting to view; as, the production of commodities, of a witness.