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Method of comparing problems by transforming one into another in computability theory
In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated
Reduction (computability theory)
Reduction_(computability_theory)
Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Concept in computability theory
In computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine
Turing_reduction
Ability to solve a problem by an effective procedure
Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical
Computability
Transformation of one computational problem to another
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently
Reduction_(complexity)
Classes of partial recursive functions
In computability theory, index sets describe classes of computable functions; specifically, they give all indices of functions in a certain class, according
Index_set_(computability)
Inherent difficulty of computational problems
analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is
Computational complexity theory
Computational_complexity_theory
Academic subfield of computer science
Recursive Functions and Effective Computability, MIT Press. ISBN 0-262-68052-1 S. Barry Cooper (2004). Computability Theory. Chapman and Hall/CRC. ISBN 1-58488-237-9
Theory_of_computation
Philosophical view explaining systems in terms of smaller parts
suggestion that a newer theory does not replace or absorb an older one, but reduces it to more basic terms. Theory reduction itself is divisible into
Reductionism
Theory of a quantum origin of consciousness
Orchestrated objective reduction (Orch OR) is a controversial theory postulating that consciousness originates at the quantum level inside neurons (rather
Orchestrated objective reduction
Orchestrated_objective_reduction
Topics referred to by the same term
compounds Ore reduction: see smelting Reduction (complexity), a transformation of one problem into another problem Reduction (recursion theory), given sets
Reduction
Yes/no problem in computer science
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a
Decision_problem
Supposition or system of ideas intended to explain something
theory — Combinatorial game theory — Computability theory — Computational complexity theory — Deformation theory — Dimension theory — Ergodic theory —
Theory
Mathematical-logic system
and =β meaning equivalence with β-reduction. See the Church–Turing thesis for other approaches to defining computability and their equivalence. Church's
Lambda_calculus
Type of computational algorithm
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually
Log-space_reduction
Framework for studying interactive computational tasks through logic
Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed
Computability_logic
Algorithm for transforming one optimization problem into another
In computability theory and computational complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is
Approximation-preserving reduction
Approximation-preserving_reduction
Type of Turing reduction
In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances
Many-one_reduction
Whether a decision problem has an effective method to derive the answer
many-one reduction in computability theory. A property of a theory or logical system weaker than decidability is semidecidability. A theory is semidecidable
Decidability_(logic)
Postpositivist communication theory developed in 1975
The uncertainty reduction theory (URT), also known as initial interaction theory, developed in 1975 by Charles Berger and Richard Calabrese, is a communication
Uncertainty_reduction_theory
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
Concept in computability theory
In computability theory, a set P of functions N → N {\displaystyle \mathbb {N} \rightarrow \mathbb {N} } is said to be Medvedev-reducible to another set
Medvedev_reducibility
Abstract machine used to study decision problems
In complexity theory and computability theory, an oracle machine is an abstract machine that can query a black box called an oracle, which is able to
Oracle_machine
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
In computability theory the Myhill isomorphism theorem, named after John Myhill, provides a characterization for two numberings to induce the same notion
Myhill_isomorphism_theorem
Thesis on the nature of computability
In computability theory, the Church–Turing thesis is a thesis about the nature of computable functions. It states that a function on the natural numbers
Church–Turing_thesis
In computability theory two sets A , B {\displaystyle A,B} of natural numbers are computably isomorphic or recursively isomorphic if there exists a total
Computable_isomorphism
Limit of a uniformly computable sequence of functions
computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in
Computation_in_the_limit
Copy of a directed graph with redundant edges removed
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges
Transitive_reduction
Type of computational problem
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a
Counting_problem_(complexity)
Concept in theoretical computer science
In computability theory, a truth-table reduction is a type of reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle
Truth-table_reduction
In computability theory, enumeration reducibility (or e-reducibility for short) is a specific type of reducibility. Roughly speaking, A is enumeration-reducible
Enumeration_reducibility
Interpretation of quantum mechanics
Objective-collapse theories, also known as spontaneous collapse models or dynamical reduction models, are proposed solutions to the measurement problem
Objective-collapse_theory
In computability theory, a subset of the natural numbers is called simple if it is computably enumerable (c.e.) and co-infinite (i.e. its complement is
Simple_set
Turing machine that halts for any input
In computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machine as it represents a total
Decider_(Turing_machine)
Overview of and topical guide to logic
rich theory that is still being actively researched. Alpha recursion theory Arithmetical set Church–Turing thesis Computability logic Computable function
Outline_of_logic
Password cracking dataset
(rambo doesn't appear in the table), one computes a chain with the two last reductions (these two reductions are represented at step 2) Note: If this
Rainbow_table
Quickly growing function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable
Ackermann_function
American mathematician (1932–2021)
reducibility" for a computability theory currently called the many-one reduction. His thesis was titled Degrees of Computability and was published in
Norman_Shapiro
Algorithm for fast modular multiplication
Montgomery form means that computing a single product by Montgomery multiplication is slower than the conventional or Barrett reduction algorithms. However,
Montgomery modular multiplication
Montgomery_modular_multiplication
Topics referred to by the same term
particular unit in USB hubs tt-reduction (truth-table reduction), a kind of transformation used in computability theory <tt>...</tt> (short for teletype)
TT
Algorithm in computational number theory
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Branch of mathematical logic
classical theories relative to constructive ones. Successful functional interpretations have yielded reductions of infinitary theories to finitary theories and
Proof_theory
Function computable with bounded loops
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all
Primitive_recursive_function
Computer hardware technology that uses quantum mechanics
can be simulated by a Turing machine. Quantum computers provide no computability power over classical computers. Thus, quantum computers cannot solve
Quantum_computing
Complexity class
least one y for which P(x,y) holds. Elaine Rich, Automata, Computability and Complexity: Theory and Applications, Prentice Hall, 2008, ISBN 0-13-228806-0
FNP_(complexity)
Measure of algorithmic complexity
14words". It is also possible to show the non-computability of K by reduction from the non-computability of the halting problem H, since K and H are Turing-equivalent
Kolmogorov_complexity
Type of set in mathematics
of Computability theory and related to algorithmic information theory in computer science. At the same time, K-trivial sets are close to computable. For
K-trivial_set
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely
NP-completeness
Concept in mathematics
classified by Dynkin diagrams, as in the theory of compact Lie groups or complex semisimple Lie algebras. Reductive groups over an arbitrary field are harder
Reductive_group
Mathematical construct in computer algebra
of the reduction by considering only the S-polynomials. This is a fundamental fact for Gröbner basis theory and all algorithms for computing them. For
Gröbner_basis
Mathematical operation
classic problem in number theory. In a little sidenote to a book review in 1831, Gauss mentions that the reduction theory for certain quadratic forms
Lattice_reduction
Technique in mathematical modeling
systems. By a reduction of the model's associated state space dimension or degrees of freedom, an approximation to the original model is computed which is
Model_order_reduction
Theorem in computability theory
In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the
Rice's_theorem
Computational problems no algorithm can solve
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist
List_of_undecidable_problems
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
Unified field theory
In physics, Kaluza–Klein theory (KK theory) is an attempt at creating a unified field theory of gravitation and electromagnetism based on the idea of
Kaluza–Klein_theory
Extension of recursion theory to admissible ordinals beyond the natural numbers
\Sigma } is from the Lévy hierarchy. There is a generalization of limit computability to partial α → α {\displaystyle \alpha \to \alpha } functions. A computational
Alpha_recursion_theory
Complexity class
(2008). "28.10 "The problem classes FP and FNP"". Automata, computability and complexity: theory and applications. Prentice Hall. pp. 689–694. ISBN 978-0-13-228806-4
FP_(complexity)
Mathematical theory of data types
theories that allow for lambda terms also include inference rules known as β {\displaystyle \beta } -reduction and η {\displaystyle \eta } -reduction
Type_theory
Notion in computational complexity theory
computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves the
Parsimonious_reduction
Integrated circuit technology
Neuromorphic computing is a computing approach inspired by the human brain's structure and function. It uses artificial neurons to perform computations
Neuromorphic_computing
Property of rewriting systems in mathematics
39:472-482, 1936 Baader & Nipkow 1998, p. 9. Cooper, S. B. (2004). Computability theory. Boca Raton: Chapman & Hall/CRC. p. 184. ISBN 1584882379. Baader
Confluence (abstract rewriting)
Confluence_(abstract_rewriting)
Mathematical model of computation
[1989]. Computability and Logic (3rd ed.). Cambridge, England: Cambridge University Press. ISBN 978-0-521-20402-6. Brookshear, J. Glenn (1989). Theory of Computation:
Finite-state_machine
Branch of mathematics
to compute some topological properties from the mapped rings than from the original spaces or schemes. Examples of results gleaned from the K-theory approach
K-theory
Topics referred to by the same term
assembly Lenstra–Lenstra–Lovász lattice basis reduction algorithm, a polynomial time lattice reduction algorithm Lowest Landau level, wave functions in
LLL
Category of mathematical proof
Emil Post that discussed the reduction of an algorithm to a simple machine-like "method" very similar to Turing's computing machine model (see Post–Turing
Proof_of_impossibility
Abstract calculator
Introduction to Computability, Addison–Wesley, 1977. Marvin Minsky, (1961), Recursive Unsolvability of Post's problem of 'Tag' and other Topics in Theory of Turing
Post–Turing_machine
Solution of some Diophantine equation
quantification merely reflects the usual applications in computability theory and model theory. It does not matter whether natural numbers refer to the
Diophantine_set
Subfield of information theory and computer science
information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail
Algorithmic information theory
Algorithmic_information_theory
Connection between correlation functions and the S-matrix
In quantum field theory, the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula is a method to calculate S-matrix elements (the scattering amplitudes)
LSZ_reduction_formula
Standard model in theoretical computer science
In computational complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs
Arithmetic_circuit_complexity
Approach to formal semantics
be special fragments of computability logic, obtained merely by disallowing certain groups of operators or atoms. Computability logic Dependence logic
Game_semantics
Concept in computability theory
In computability theory, a set P {\displaystyle P} of functions N → N {\displaystyle \mathbb {N} \rightarrow \mathbb {N} } is said to be Mučnik-reducible
Mučnik_reducibility
of dimension at least two is often called geometric class field theory. Good reduction Fundamental to local analysis in arithmetic problems is to reduce
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Theory of machine learning
In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and
Computational_learning_theory
cone lemma from computability theory. The Wadge game is a simple infinite game used to investigate the notion of continuous reduction for subsets of Baire
Wadge_hierarchy
American mathematician and logician (1897 – 1954)
known for his work in the field that eventually became known as computability theory. Post was born in Augustów, Suwałki Governorate, Congress Poland
Emil_Leon_Post
Computer science concept
subset of the array, and the reduction operator merges the results. Using a binary tree reduction would allow 4 cores to compute ( 2 + 3 ) {\textstyle (2+3)}
Reduction_operator
Algorithm in modular arithmetic
< n {\displaystyle a,b<n} , one computed a b mod n {\displaystyle ab\,{\bmod {\,}}n\,} by applying Barrett reduction to the full product a b {\displaystyle
Barrett_reduction
with respect to the computability-logic semantics. In "On the system CL12 of computability logic", on the platform of computability logic, Japaridze generalized
Giorgi_Japaridze
Projection of data onto lower-dimensional manifolds
candidate for dimensionality reduction of the dynamical system. While such manifolds are not guaranteed to exist in general, the theory of spectral submanifolds
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Process by which a quantum system takes on a definitive state
measurements of a quantum system give the same results, the theory postulates a "collapse" or "reduction of the state vector" upon observation, abruptly converting
Wave_function_collapse
Barry Cooper (2004). Computability Theory. Chapman & Hall. ISBN 1-58488-237-9. Herbert Enderton (2011). Computability Theory. Academic Press. ISBN 978-0-12-384-958-8
PR_(complexity)
Overview of and topical guide to machine learning
evolved from the study of pattern recognition and computational learning theory. In 1959, Arthur Samuel defined machine learning as a "field of study that
Outline_of_machine_learning
Branch of ordinary differential equations
results in a combination of underlying periodicity and growth. Floquet theory provides a way to analyze such systems. Its essential insight is similar
Floquet_theory
American mathematician (1919–1985)
mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on
Julia_Robinson
Family of optimization algorithms
is among the most popular of the variance reduction methods due to its simplicity, easily adaptable theory, and excellent performance. It is the successor
Stochastic_variance_reduction
Area of mathematics
representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be
Representation theory of the symmetric group
Representation_theory_of_the_symmetric_group
Sequence of operations for a task
of algorithms Regulation of algorithms Theory of computation Computability theory Computational complexity theory "A procedure which has all the characteristics
Algorithm
Length of shortest path between two nodes of a graph
In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph
Distance_(graph_theory)
Topics referred to by the same term
expression, vocalization, and posture Affect theory Affective science, the scientific study of emotion Affective computing, an area of research in computer science
Affect
Database theory algorithm
query, a join tree exists and can be computed in linear time; one standard way to obtain it is via the GYO reduction. The nodes of the join tree correspond
Yannakakis_algorithm
Mathematical study of invariants under symmetries
circle of ideas is given by the theory of standard monomials. Simple examples of invariant theory come from computing the invariant monomials from a group
Invariant_theory
Existence of values making formula true
(MIT Press). Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Daniel Kroening; Ofer
Satisfiability
Book by Roger Penrose
the limits of computability. The human mind has abilities that no Turing machine could possess because of this mechanism of non-computable physics. In 1931
Shadows_of_the_Mind
Mathematical proof about the permanent of matrices
result in computational complexity theory. In 1979, Leslie Valiant proved that the computational problem of computing the permanent of a matrix is #P-hard
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
Theory within consciousness research
Integrated information theory (IIT) proposes a mathematical model for the consciousness of a system. It comprises a framework ultimately intended to explain
Integrated_information_theory
American computer scientist
termination analysis. Within the theory of computation, he was among the pioneers of the study of Log-space reductions and P-completeness. Neil D. Jones
Neil_D._Jones
Numerical method that reduces the complexity of computationally intensive simulations
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
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
Boy/Male
Tamil
Education
Girl/Female
Indian, Telugu
Good Education
Girl/Female
Tamil
Sarsvati | ஸரஸà¯à®µà®¤à¯€
Goddess of education
Sarsvati | ஸரஸà¯à®µà®¤à¯€
Girl/Female
Indian, Marathi
Education
Girl/Female
Arabic
Culture; Education
Girl/Female
Hindu
Modesty, Education
Girl/Female
Tamil
Education
Girl/Female
Indian, Punjabi, Sikh
Natural; Education
Girl/Female
Hindu, Indian, Tamil
Education
Boy/Male
Indian
Education
Boy/Male
Arabic, Muslim
Education
Boy/Male
Muslim
Sky, Education, Instruction
Girl/Female
Tamil
Education
Boy/Male
Arabic, Muslim
Education; Instruction
Girl/Female
Indian
Education
Girl/Female
Tamil
Modesty, Education
Girl/Female
Arabic
Culture; Education
Girl/Female
Hindu
Education
Boy/Male
Tamil
Vidyesh | விதà¯à®¯à¯‡à®·Â
Vidya--education esh-ishwar--god --god of education
Vidyesh | விதà¯à®¯à¯‡à®·Â
Boy/Male
Hindu
Vidya--education esh-ishwar--god --god of education
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
Boy/Male
Tamil
Belavardhana | பேலாவாரà¯à®¤à®¾à®¨à®¾
One of the kauravas
Boy/Male
British, English
Welsh Friend
Boy/Male
English
Anne's son; son of God. Famous Bearer: actor Anson Williams.
Boy/Male
Greek
Dragon of Hera.
Surname or Lastname
English
English : unexplained.
Girl/Female
American, Australian, Christian, French, German, Greek, Jamaican, Teutonic
Healthy; Wide; Famous in War; Renowned in Battle; Hale; Sun; Intelligent; Smart; Fighter; Warrior; Similar to Louise Famous in War
Boy/Male
Gaelic
Horse lord.
Boy/Male
Latin Italian Shakespearean Spanish
Of the Adriatic.
Boy/Male
Hindu, Indian
Easy
Male
Serbian
Serbian form of Greek Ioseph, JOSIF means "(God) shall add (another son)."Â
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
REDUCTION COMPUTABILITY-THEORY
n.
The act or process of inferring by deduction or induction.
n.
The quality or power of being compatible or congruous; congruity; as, a compatibility of tempers; a compatibility of properties.
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 amount abated; that which is taken away by way of reduction; deduction; decrease; a rebate or discount allowed.
n.
A reductive agent.
n.
The act or process or producing, bringing forth, or exhibiting to view; as, the production of commodities, of a witness.
n.
The action by which the parts of the body are drawn towards its axis]; -- opposed to abduction.
n.
A red crystalline nitrogenous substance or artificial production, which by reduction passes directly to indigo.
n.
Reduction.
n.
That which seduces, or is adapted to seduce; means of leading astray; as, the seductions of wealth.
n.
The wrongful, and usually the forcible, carrying off of a human being; as, the abduction of a child, the abduction of an heiress.
v. t.
The operation of restoring a dislocated or fractured part to its former place.
n.
Compatibility; consistency; fitness; agreement.
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.
That which is deducted; the part taken away; abatement; as, a deduction from the yearly rent.
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.
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 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.
The quality of being commutable.