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Compound operation in relational databases
The recursive join is an operation used in relational databases, also sometimes called a "fixed-point join". It is a compound operation that involves repeating
Recursive_join
queries are a specific kind of recursive query in graph databases Deductive databases Hierarchical model Recursive join Reachability Transitive closure
Hierarchical and recursive queries in SQL
Hierarchical_and_recursive_queries_in_SQL
Process where AI repeatedly improves itself
Recursive self-improvement (RSI) is a process in which an artificial intelligence (AI) system iteratively designs a more capable successor. This may trigger
Recursive_self-improvement
Algorithm used in relational databases
hash join is an example of a join algorithm and is used in the implementation of a relational database management system. All variants of hash join algorithms
Hash_join
Way of setting up and executing parallel computer programs
in the program, to "join" (merge) at a subsequent point and resume sequential execution. Parallel sections may fork recursively until a certain task
Fork–join_model
Higher-order function which returns some fixed point of the input function
describe specific types of recursive computations, such as those in fixed-point iteration, iterative methods, recursive join in relational databases, data-flow
Fixed-point_combinator
Topics referred to by the same term
point, a benchmark (surveying) used by geodesists Fixed point join, also called a recursive join Fixed point, in quantum field theory, a coupling where the
Fixed_point
American AI entrepreneur (born 1983)
Amodei has also called for a slowdown of AI development, especially recursive self-improvement by democratic states, while engaging China in arms control-analogous
Dario_Amodei
Algorithms which recursively solve subproblems
designates an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related
Divide-and-conquer_algorithm
Rendering method
fidelity, ray tracing-based rendering techniques, such as ray casting, recursive ray tracing, distribution ray tracing, photon mapping and path tracing
Ray_tracing_(graphics)
Computer network architecture proposal
The Recursive InterNetwork Architecture (RINA) is a new computer network architecture proposed as an alternative to the architecture of the currently
Recursive Internetwork Architecture
Recursive_Internetwork_Architecture
Random search tree data structure
probability proportional to its number of descendants, and the join proceeds recursively. The information stored per node in the randomized binary tree
Treap
Graph formed by complementation and disjoint union
Alternatively, instead of using the complement operation, one can use the join operation, which consists of forming the disjoint union G∪H and then adding
Cograph
AI researcher and entrepreneur (born 1983)
search infrastructure company, and co-founder and CEO of Recursive, a company pursuing recursive self-improvement. He is also a co-founder and investment
Richard_Socher
Australian psychologist (born 1958)
and the safety of vaccines. On 28 March 2013, Lewandowsky published "Recursive fury: Conspiracist ideation in the blogosphere in response to research
Stephan_Lewandowsky
Automated methods for the creation of mazes
and one for the exit, are removed. This algorithm, also known as the "recursive backtracker" algorithm, is a randomized version of the depth-first search
Maze_generation_algorithm
Hypothesized risk to human existence
replacement, even at the cost of human lives. Researchers warn that a rapid, recursive cycle of AI self-improvement could boost AI capabilities too quickly for
Existential risk from artificial intelligence
Existential_risk_from_artificial_intelligence
Algorithm that estimates unknowns from a series of measurements over time
more weight given to estimates with greater certainty. The algorithm is recursive. It can operate in real time, using only the present input measurements
Kalman_filter
Type of binary relation
called transfinite induction. When the well-founded set is a set of recursively defined data structures, the technique is called structural induction
Well-founded_relation
Mathematical technique used in proof theory
being analyzed, for example characterizations of the classes of provably recursive, hyperarithmetical, or Δ 2 1 {\displaystyle \Delta _{2}^{1}} functions
Ordinal_analysis
Mathematical puzzle game
of disks is even and peg C if it is odd. The key to solving a problem recursively is to recognize that it can be broken down into a collection of smaller
Tower_of_Hanoi
and return a tree containing all selected entries. It recursively filters the two subtrees, and join them with the root if the root satisfies p {\displaystyle
Join-based_tree_algorithms
Mathematical concept for comparing objects
order relations. The arguments of the lattice theory operations meet and join are elements of some universe A. Meanwhile, the arguments of the transformation
Equivalence_relation
American artificial intelligence company
down "borderline crazy" offers of two to three times his market value to join OpenAI instead. In April 2016, OpenAI released a public beta of "OpenAI Gym"
OpenAI
Social media app
launched in June 2025 by Recursive Methods Pty Ltd. It was founded by Issam Hijazi. UpScrolled was launched in June 2025 by Recursive Methods Pty Ltd. It was
UpScrolled
Measure of unsolvability
⟨ ≤, = ⟩. A degree is called recursively enumerable (r.e.) or computably enumerable (c.e.) if it contains a recursively enumerable set. Every r.e. degree
Turing_degree
Country in Southeastern and Central Europe
5B Boom: Can Serbia's Tech Ecosystem Navigate its Own Success?". The Recursive. Retrieved 10 August 2026. "Serbia plans major expansion of state data
Serbia
Rooted binary tree data structure
pseudocode implements the BST search procedure through recursion. The recursive procedure continues until a nil {\displaystyle {\text{nil}}} or the key
Binary_search_tree
Curve used in computer graphics and related fields
with these properties. Bézier curves can be defined for any degree n. A recursive definition for the Bézier curve of degree n expresses it as a point-to-point
Bézier_curve
Mathematical proposition equivalent to the axiom of choice
is defined using transfinite recursion. It is exactly like the usual recursive definition of a sequence but runs over ordinals. A key difference is that
Zorn's_lemma
Chinese text-to-video model
United States". The New York Times. Retrieved 20 September 2025. "ByteDance joins OpenAI's Sora rivals with AI video app launch". Reuters. 6 August 2024.
Kling_AI
Infinitely recursive poem or song
"Yon Yonson" or "Jan Jansen" is an infinitely recursive folk song, most popular in the midwestern United States. The song being set in Wisconsin is a
Yon_Yonson
Large number coined by Ronald Graham
computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula
Graham's_number
Internet ecosystem layer that addresses bottlenecks
availability, and cost. Traditionally, CDNs have used the IP of the client's recursive DNS resolver to geo-locate the client. While this is a sound approach
Content_delivery_network
Smallest transitive relation containing a given binary relation
declarative query. The SQL 3 (1999) standard added a more general WITH RECURSIVE construct also allowing transitive closures to be computed inside the
Transitive_closure
Formal power series
two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant coefficients; this generalizes the examples above
Generating_function
Divide and conquer sorting algorithm
parallelization of those recursive calls. Following pseudocode describes the merge sort with parallel recursion using the fork and join keywords: // Sort elements
Merge_sort
Statement that is taken to be true
context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms Σ of the Theory of Arithmetic is
Axiom
Compiler-compiler
In computing, TMG (Transmogrifier) is a recursive descent compiler-compiler developed by Robert M. McClure and presented in 1965. TMG ran on systems including
TMG_(language)
Diagram that represents a workflow or process
flowcharts are not well-suited for new programming techniques such as recursive programming. Nevertheless, flowcharts were still used in the early 21st
Flowchart
Algebraic manipulation of "true" and "false"
Whitespace is used to specify logical AND, as it is the default operator for joining search terms: "Search term 1" "Search term 2" The OR keyword is used for
Boolean_algebra
Autonomous artificial intelligence agent
companies' CEOs stated in early 2025 that they expect AI agents to eventually "join the workforce". However, in a preprint study, Carnegie Mellon University
AI_agent
Default package manager for the JavaScript runtime environment Node.js
understood to be an abbreviation of "Node Package Manager", it is officially a recursive backronymic abbreviation for "npm is not an acronym". npm can manage packages
Npm
to provide a platform for discussion of artificial intelligence. Apple joined in January 2017. The corporate members will make financial and research
Ethics of artificial intelligence
Ethics_of_artificial_intelligence
JavaScript JCL JEAN Jess Join Java JOSS Joule JOVIAL Joy jq JScript JScript .NET Julia Jython K Kaleidoscope Karel KEE Kent Recursive Calculator (KRC) KiXtart
List_of_programming_languages
Scripting language created in 1994
originally an abbreviation of "Personal Home Page", but it now stands for the recursive backronym "PHP: Hypertext Preprocessor". PHP code is usually processed
PHP
2023 business action in the US
(November 20, 2023). "Hundreds of OpenAI employees threaten to resign and join Microsoft". The Verge. Archived from the original on November 20, 2023. Retrieved
Removal of Sam Altman from OpenAI
Removal_of_Sam_Altman_from_OpenAI
researchers outside these institutions and the many thousands that were joining the field were unaffected. Several philosophers had strong objections to
History of artificial intelligence
History_of_artificial_intelligence
Self-balancing binary search tree data structure
divide-and-conquer implementation of the join-based algorithm for bulk-insert. Both recursive calls can be executed in parallel. The join operation used here differs
Red–black_tree
Self-balancing binary search tree
of the tree. If the tree is not empty, then we go down the root, and recursively go down the tree searching for the location to insert the new node. This
AVL_tree
RDF query language
SPARQL (pronounced "sparkle", a recursive acronym for SPARQL Protocol and RDF Query Language) is an RDF query language—that is, a semantic query language
SPARQL
Mathematical system
zero or a successor") Addition defined recursively: ∀m[m+0=m]. ∀m∀n[m+Sn=S(m+n)]. Multiplication defined recursively: ∀m[m⋅0=0]. ∀m∀n[m⋅Sn=(m⋅n)+m]. Axioms
Second-order_arithmetic
Algorithm to multiply matrices
the recurrence T(1)=Θ(1); T(n)=8T(n/2)+Θ(n2), accounting for the eight recursive calls on matrices of size n/2 and Θ(n2) to sum the four pairs of resulting
Matrix multiplication algorithm
Matrix_multiplication_algorithm
American AI researcher and writer (born 1979)
In the intelligence explosion scenario hypothesized by I. J. Good, recursively self-improving AI systems quickly transition from subhuman general intelligence
Eliezer_Yudkowsky
Species of hominid in the genus Homo
only animals known to teach generalizable information, innately deploy recursive embedding to generate and communicate complex concepts, engage in the
Human
2025 video game
that a sequel to Wuchang: Fallen Feathers would be developed by Chengdu Recursive Dolphin Technology and published by 505 Games. The development studio
Wuchang:_Fallen_Feathers
French professional Valorant player
added kennyS, Maniac, and Uzzziii to the team. This squad was signed by Recursive eSports before the first CS:GO Major sponsored by Valve, DreamHack Winter
Happy_(gamer)
Well-quasi-ordering of finite trees
as a function of n {\displaystyle n} , far faster than any primitive recursive function or the Ackermann function, for example.[citation needed] The
Kruskal's_tree_theorem
Video game publisher
Retrieved September 4, 2020. Wales, Matt (February 8, 2021). "Annapurna's recursive puzzle adventure Maquette gets March release date". Eurogamer. Archived
Annapurna_Interactive
Characters of 2023 role-playing video game
Wēngfǎluósī; 'Omphalos') is an isolated, simulated planet. It is the result of a recursive experiment managed by Lygus with the purpose of bringing forth Irontomb
List of Honkai: Star Rail characters
List_of_Honkai:_Star_Rail_characters
Mathematician and philosopher (1906–1978)
the ideas of computability and recursive functions to the point that he was able to present a lecture on general recursive functions and the concept of
Kurt_Gödel
Theoretical physicist and artificial intelligence researcher
decide by 2030 whether to take the risk of giving AI the autonomy to recursively improve itself, which he said could be beneficial but could also lead
Jared_Kaplan
Overview of and topical guide to algorithms
iterative algorithms Recurrence relation — equation often used to analyze recursive algorithms Master theorem (analysis of algorithms) — theorem for solving
Outline_of_algorithms
Identities and relationships involving sets
closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection, the complement
Algebra_of_sets
Free and open-source object relational database management system
Views Materialized views Updateable views Recursive views Inner, outer (full, left, and right), and cross joins Sub-selects Correlated sub-queries Regular
PostgreSQL
Voting systems that use ranked ballots
ranked-choice voting in general, is a contingent ranked-vote voting method that recursively eliminates the successive plurality loser during rounds of counting and
Ranked_voting
American computer scientist and mathematician (born 1938)
bachelor's degree. Impressed by the ALGOL syntax chart, symbol table, recursive-descent approach, and the separation of the scanning, parsing, and emitting
Donald_Knuth
Fourier-related transform for signals that change over time
x_{1}(q)={\begin{cases}x((n-Q+q)\Delta _{t})&q\leq 2Q\\0&q>2Q\end{cases}}} Applying the recursive formula to calculate X ( n Δ t , m Δ f ) {\displaystyle X(n\Delta _{t}
Short-time_Fourier_transform
American mathematician (1909–1994)
(1936). "General recursive functions of natural numbers". Mathematische Annalen (112): 727–742. —— (1936a). "λ-definability and recursiveness". Duke Mathematical
Stephen_Cole_Kleene
Union data structure with enforced cases
correctly when that type is manipulated. This is critical in defining recursive datatypes, in which some component of a value may have the same type as
Tagged_union
1995 film by Kim Henkel
film scholars have noted the film's prominent elements of parody and recursiveness. In the years since its release, the film has gone on to develop a small
The Return of the Texas Chainsaw Massacre
The_Return_of_the_Texas_Chainsaw_Massacre
American scientist (1927–2011)
logic programming. In the late 1950s, McCarthy discovered that primitive recursive functions could be extended to compute with symbolic expressions, producing
John McCarthy (computer scientist)
John_McCarthy_(computer_scientist)
Sequence of characters that forms a search pattern
features of Perl 5.x regexes, but also allow BNF-style definition of a recursive descent parser via sub-rules. The use of regexes in structured information
Regular_expression
Domain name system provided by Cisco
supports the DNSCurve secure protocol. OpenDNS provides the following recursive nameserver addresses for public use, mapped to the nearest operational
OpenDNS
German software company
Lenses gets acquired by enterprise software giant valued at $11B". The Recursive. October 6, 2021. Retrieved October 18, 2021. "CORRECTING and REPLACING
Celonis
Country in East Asia
Booms and Sustainable Economic Growth in Mongolia—Empirical Result from Recursive Dynamic CGE Model". Economies. 7 (2): 51. doi:10.3390/economies7020051
Mongolia
2023 video game
by Eurogamer as their Game of the Year. Holt, Kris (June 29, 2023). "Recursive puzzle adventure game 'Cocoon' will arrive on September 29th". Engadget
Cocoon_(video_game)
Browser-based graphing calculator
graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids
Desmos
2021 YouTube analog horror web series
Alex Kister 10:48 October 30, 2024 (2024-10-30) Dave Lee testing the recursive generation loss of VHS tapes, with the copies of the original tape very
The_Mandela_Catalogue
Mathematical set formed from two given sets
Cartesian product) Direct product Empty product Finitary relation Join (SQL) § Cross join Orders on the Cartesian product of totally ordered sets Outer product
Cartesian_product
Type of fiction created by fans of the original subject
Stories based on an existing fan work. On Archive of Our Own, this type of recursive fan fiction is called a "remix". Stories which are interspersed with the
Fan_fiction
American economist and Nobel Laureate (born 1943)
robust control theory. Sargent has also been a pioneer in introducing recursive economics to academic study, especially for macroeconomic issues such
Thomas_J._Sargent
American computer scientist (born 1932)
with Douglas E. Eastwood of Bell Labs, he introduced conditional and recursive macros into popular SAP assembler, creating what is known as Macro SAP
Douglas_McIlroy
German polymath and scholar (1777–1855)
Adrien-Marie Legendre published it. Gauss also introduced the algorithm known as recursive least squares. Gauss led the geodetic survey of the Kingdom of Hanover
Carl_Friedrich_Gauss
Israeli cryptographer (born 1952)
Rivest Weizmann Institute Shamir, Adi (October 1976). The fixedpoints of recursive definitions. Weizmann Institute of Science. OCLC 884951223. Adi Shamir
Adi_Shamir
American AI safety researcher
Nissan; Lowe, Ryan; Leike, J.; Christiano, P. (September 22, 2021). "Recursively Summarizing Books with Human Feedback". arXiv:2109.10862 [cs.CL]. Christiano
Paul_Christiano
Video game character
trajectory. The current Flame-Chase Journey is already the 33,550,336th recursive loop of the cycle involving Phainon's generation. Before this loop known
Phainon_(Honkai:_Star_Rail)
ISO 4396 Telecommunications and information exchange between systems — Recursive inter-network architecture [Original DPR with this number related to fluid
List of ISO standards 3000–4999
List_of_ISO_standards_3000–4999
1969 non-fiction book by G. Spencer-Brown
interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA). "Boundary algebra" is a Meguire (2011) term for the
Laws_of_Form
Chinese artificial intelligence company
Retrieved 24 August 2024. Zhang, Jane (20 October 2023). "Alibaba, Tencent Join Big Backers for Chinese AI Startup Zhipu". Bloomberg.com. Retrieved 24 August
Z.ai
1994 film by Quentin Tarantino
between the intricate plot mechanics and twists of Brown's novels and the recursive, interweaving structure of Pulp Fiction. Philip French describes the film's
Pulp_Fiction
American computer scientist
textbooks, including Thinking Recursively The Art and Science of C Programming Abstractions in C Thinking Recursively with Java The Art and Science of
Eric_S._Roberts
Arithmetic operation
where A∪B means the union of A and B.. The other popular definition is recursive: Let n+ be the successor of n, that is the number following n in the natural
Addition
Flanders and Swann, which is sung by a gnu. It is also an early example of a recursive acronym: "GNU's Not Unix". Google – a search engine. The name started
List of computer term etymologies
List_of_computer_term_etymologies
Branch of machine learning
of as probabilistic context free grammar (PCFG) implemented by an RNN. Recursive auto-encoders built atop word embeddings can assess sentence similarity
Deep_learning
WordPress hosting and technology company
(2024-07-18). "Bulgarian Company NitroPack Acquired by US WP Engine". TheRecursive.com. Retrieved 2024-08-25. Montti, Roger (2024-07-19). "WP Engine WordPress
WP_Engine
Declarative logic programming language
ancestor of? For this example, it would return brooke and damocles. The non-recursive subset of Datalog is closely related to query languages for relational
Datalog
Concept in computer science
[citation needed] A closely related "where" clause, together with its recursive variant "where rec", appeared already in Peter Landin's The mechanical
Let_expression
Database model
relational model, which cannot express recursive queries without introducing a least-fixed-point operator, recursive relations can be defined in Datalog
Relational_model
Probability distribution
variable. The split normal distribution is most directly defined in terms of joining scaled sections of the density functions of different normal distributions
Normal_distribution
travel, tourism, insurance
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travel, tourism, insurance