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Recursive indexing is an algorithm used to represent large numeric values using members of a relatively small set. Recursive indexing writes the successive
Recursive_indexing
Use of functions that call themselves
solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own
Recursion_(computer_science)
Process of repeating items in a self-similar way
references can occur. A process that exhibits recursion is recursive. Video feedback displays recursive images, as does an infinity mirror. In mathematics and
Recursion
One of several equivalent definitions of a computable function
mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural
General_recursive_function
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
Form of lossless data compression
file formats Golomb coding Burrows–Wheeler transform Recursive indexing Run-length limited Bitmap index Forsyth–Edwards Notation, which uses run-length-encoding
Run-length_encoding
Compound operation in relational databases
so is more specifically a "recursive self-join". Recursive joins can be very time-consuming unless optimized through indexing, the addition of extra key
Recursive_join
Pattern defining an infinite sequence of numbers
non-recursive function of n {\displaystyle n} . The concept of a recurrence relation can be extended to multidimensional arrays, that is, indexed families
Recurrence_relation
Specification of a mathematical group by generators and relations
subset U of FS recursive (respectively recursively enumerable) if f(U) is recursive (respectively recursively enumerable). If S is indexed as above and
Presentation_of_a_group
Compact encoding of digital data
PackBits PAQ Prediction by partial matching Range coding Re-Pair Recursive indexing Rice coding Run-length encoding Sequitur algorithm Shannon coding
Data_compression
Divide and conquer sorting algorithm
sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory
Quicksort
Adaptive filter algorithm for digital signal processing
Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost
Recursive least squares filter
Recursive_least_squares_filter
Concept in computability theory
is not itself recursively enumerable. Let W e {\displaystyle W_{e}} denote the set of input values for which the Turing machine with index e halts. Then
Turing_reduction
Quickly growing function
examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function
Ackermann_function
Curve simplification algorithm
dmax) { index = i dmax = d } } ResultList[] = empty; # If max distance is greater than epsilon, recursively simplify if (dmax > epsilon) { # Recursive call
Ramer–Douglas–Peucker algorithm
Ramer–Douglas–Peucker_algorithm
Concept in computability theory
disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set. These
Computably_inseparable
Limit of a uniformly computable sequence of functions
sequence of functions. The terms computable in the limit, limit recursive and recursively approximable are also used. One can think of limit computable
Computation_in_the_limit
Computer science and linguistics concept relating to non-terminal production
science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according
Recursive_grammar
Study of computable functions and Turing degrees
mathematical constructions can be effectively performed is sometimes called recursive mathematics. Computability theory originated in the 1930s, with the work
Computability_theory
Problem optimization method
break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding
Dynamic_programming
Limited form of tree data structure
child and the right child. That is, it is a k-ary tree where k = 2. A recursive definition using set theory is that a binary tree is a triple (L, S, R)
Binary_tree
index. Deep indexing is used when multiple clauses use the same principal functor for some argument. It recursively uses the same or similar indexing
Term_indexing
Theorem in computability theory
defined via recursive definitions. The statement of the theorems refers to an admissible numbering φ {\displaystyle \varphi } of the partial recursive functions
Kleene's_recursion_theorem
Computer data structure
called a multi-vantage-point tree (or MVP tree): a data structure for indexing objects from large metric spaces for similarity search queries. It uses
Vantage-point_tree
Infinite sequence of numbers satisfying a linear equation
… {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant-recursive if it satisfies an equation of the form s n = c 1 s n − 1 + c 2 s n −
Constant-recursive_sequence
Software that systematically browses the World Wide Web
Python. The crawler was integrated with the indexing process, because text parsing was done for full-text indexing and also for URL extraction. There is a
Web_crawler
Compressed data structure for pattern matching
the 0 t h {\displaystyle 0^{th}} -order entropy and that the index supports self-indexing. The space bound was further improved achieving the ultimate
Compressed_suffix_array
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
Package management system for Python
received on his blog post. According to Bicking himself, the name is a recursive acronym for "Pip Installs Packages". In 2011, the Python Packaging Authority
Pip_(package_manager)
Templates in computer programming
less[further explanation needed] recursive syntax, while the index is required to be a constant expression. The syntax of pack indexing is id-expression...[expression]
Variadic_template
Statistical term, a compound measure in statistics
the OECD high level statistical committee, describe ten recursive steps for developing an index: Step 1: Theoretical framework Step 2: Data selection Step
Index_(statistics)
Tree-based computer data structure
index to minimize the number of disk reads uses partially full blocks to speed up insertions and deletions keeps the index balanced with a recursive algorithm
B-tree
Branch of mathematical logic
reverse mathematics. The initials "RCA" stand for "recursive comprehension axiom", where "recursive" means "computable", as in computable function. This
Reverse_mathematics
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
Classes of partial recursive functions
Elsevier. p. 668. ISBN 0-444-89483-7. Rogers Jr., Hartley (1987). Theory of Recursive Functions and Effective Computability. MIT Press. p. 482. ISBN 0-262-68052-1
Index_set_(computability)
Higher-order function that combines several parsers
starting at index 2 and finishing at any index between 2 and 5 inclusive. Parser combinators, like all recursive descent parsers, are not limited to the
Parser_combinator
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
Technique for defining number-theoretic functions by recursion
1-ary primitive recursive function g the value of g(n+1) is computed only from g(n) and n. The factorial function n! is recursively defined by the rules
Course-of-values_recursion
Desktop search tool
of inotify. Recoll updates its index at designed intervals (for example, through cronjobs), but if desired, the indexing task can run as a file-system
Recoll
Problem in computer science
0′ (the "jump" of class 0) representing the class of recursively enumerable, but not recursive, sets of numbers, or similarly Σ 1 0 {\displaystyle \Sigma
Halting_problem
Mathematical-logic system
is M; this means a recursive function definition cannot be written with let. The letrec construction would allow writing recursive function definitions
Lambda_calculus
Data structure
metadata indexing; BFS also uses B+ trees for storing directories. NTFS uses B+ trees for directory and security-related metadata indexing. EXT4 uses
B+_tree
Axiom of set theory
sequence (i.e., countable indexed family) of nonempty sets is nonempty. (This is just the axiom of choice with the indexing set restricted to countable
Axiom_of_choice
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
Arithmetic operation
Goodstein in his 1947 paper Transfinite Ordinals in Recursive Number Theory (generalizing the recursive base-representation used in Goodstein's theorem to
Tetration
Academic subfield of computer science
μ-recursive functions a computation consists of a mu-recursive function, i.e. its defining sequence, any input value(s) and a sequence of recursive functions
Theory_of_computation
Academic journal
Norwegian Scientific Index. Retrieved 2019-12-04. Lewandowsky, Stephan; Cook, John; Oberauer, Klaus; Marriott, Michael (2013). "Recursive fury: Conspiracist
Frontiers_in_Psychology
3rd–2nd century BC Indian mathematician and poet
syllable sequence, given the rank/index number of a meter. Uddiṣṭa (Indexing): The inverse algorithm to find the rank/index number of a given sequence of
Pingala
Class of algorithms
current node. Recursively traverse the current node's right subtree. Recursively traverse the current node's left subtree. Recursively traverse the current
Tree_traversal
Method in natural language processing
Magnus (2005) An Introduction to Random Indexing, Proceedings of the Methods and Applications of Semantic Indexing Workshop at the 7th International Conference
Word_embedding
Family of higher-order functions
function that analyzes a recursive data structure and, through use of a given combining operation, recombines the results of recursively processing its constituent
Fold_(higher-order_function)
Fast Fourier Transform algorithm
separating out relatively prime factors. The algorithm, along with its recursive application, was invented by Carl Friedrich Gauss. Cooley and Tukey independently
Cooley–Tukey_FFT_algorithm
Concept in computability theory
number with a given property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose
Mu_operator
Computing term
color depth). Pixels of 8 bits and fewer can represent either grayscale or indexed color. An alpha channel (for transparency) may be stored in a separate
Bitmap
Organization of information or objects into (usually self-similar) layers
to self-similar or recursive structures in some sense. Nesting can mean: nested calls: using several levels of subroutines recursive calls nested levels
Nesting_(computing)
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
Processing of scanned text document
the layout of the document. Examples of top-down approaches include the recursive X-Y cut algorithm, which decomposes the document in rectangular sections
Document_layout_analysis
Control flow construct for executing code repeatedly
until a program terminates, such as web servers. Primitive recursive function General recursive function Repeat loop (disambiguation) LOOP (programming language)
Loop_(statement)
Data structure in computer science
Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional
Octree
Design technique for parallel algorithms
pointer jumping is considered a software design pattern for operating on recursive data types in parallel. As a technique for following linked paths, graph
Pointer_jumping
Computer science and recursion theory
of recursive functions by use of the IF-THEN-ELSE construction common to computer science, together with four of the operators of primitive recursive functions:
McCarthy_Formalism
Type of a context-free grammar
characterized as precisely those that can be parsed by a predictive parser – a recursive descent parser without backtracking – and these can be readily written
LL_grammar
Data structures used in spatial indexing
R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles
R-tree
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)
Turing machine that halts for any input
class of languages that can be decided by such machines is the set of recursive languages. Given an arbitrary Turing machine, determining whether it is
Decider_(Turing_machine)
Algorithm that arranges lists in order
"in-place". Recursion: Some algorithms are either typically recursive or typically non-recursive, while others may typically be both (e.g., merge sort). Stability:
Sorting_algorithm
Algorithm to compare text strings using wildcard syntax
in zero-based indices, the wildcard-matching problem can be defined recursively as: m 00 = ( p 0 = t 0 ) m 0 j = false m i 0 = ( p i − 1 = ‘*’ ) ∧ m
Matching_wildcards
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
Partition of Earth's surface into subdivided cells
in the grid is called a cell. When each cell of a grid is subject to a recursive partition, resulting in a "series of discrete global grids with progressively
Discrete_global_grid
Programming language that uses first order logic
linear in the number of clauses. Term indexing uses a data structure that enables sub-linear-time lookups. Indexing only affects program performance, it
Prolog
Encoded data represented in binary notation
An example of a recursive binary space partitioning quadtree for a 2D index
Binary_code
Structure of a formal language
practical language translation tools. A recursive grammar is a grammar that contains production rules that are recursive. For example, a grammar for a context-free
Formal_grammar
Type of mathematical function
numbers. A recursive ordinal notation must satisfy the following two additional properties: the subset of natural numbers is a recursive set the induced
Ordinal_notation
Measure in decision theory
S2CID 656323. Sonin I (2008). "A generalized Gittins index for a Markov chain and its recursive calculation". Statistics and Probability Letters. 78 (12):
Gittins_index
Free and open-source object relational database management system
create their own data types which can usually be made fully indexable via PostgreSQL's indexing infrastructures – GiST, GIN, SP-GiST. Examples of these include
PostgreSQL
Class of artificial neural network
logical terms. A special case of recursive neural networks is the RNN whose structure corresponds to a linear chain. Recursive neural networks have been applied
Recurrent_neural_network
Abstract data type
value on the stack. Stacks are an important way of supporting nested or recursive function calls. This type of stack is used implicitly by the compiler
Stack_(abstract_data_type)
Search engine from Google
search results. Despite Google search's immense index, sources generally assume that Google is only indexing less than 5% of the total Internet, with the
Google_Search
Image dithering algorithm
or, when unscaled, an index matrix. For threshold maps whose dimensions are a power of two, the map can be generated recursively via: M 2 n = 1 ( 2 n )
Ordered_dithering
Sequence of program instructions invokable by other software
hardware supports only a few levels of subroutine nesting, but can support recursive subroutines. Machines before the mid-1960s, such as the UNIVAC I, the
Function (computer programming)
Function_(computer_programming)
Type of algorithm in computer science
requires that the input of the recursive call must get smaller each time, corecursion requires that the output of the recursive call must get larger each time
Corecursion
Generates a forecast of future values of a time series
Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages
Exponential_smoothing
Theory that characterizes object complexity
'assembly space' can be defined as all recursively assembled pathways that produce this object. The 'assembly index' is the number of steps on a shortest
Assembly_theory
Type of computer science algorithm
expanded definition still excludes quicksort, however, because of its recursive calls. Identifying the in-place algorithms with L has some interesting
In-place_algorithm
Generalization of "n-th" to infinite cases
additively indecomposable ordinal is indexed as ω γ {\displaystyle \omega ^{\gamma }} . The technique of indexing classes of ordinals is often useful
Ordinal_number
Whole of an object being mathematically similar to part of itself
of a viable system one recursive level higher up, and for whom the elements of its System One are viable systems one recursive level lower down.[citation
Self-similarity
Infinitely detailed mathematical structure
nature can be modeled on a computer by using recursive algorithms and L-systems techniques. The recursive nature of some patterns is obvious in certain
Fractal
Type of computer arithmetic
c_{j}<a_{j}} . To find the actual values in these sequences, we use a set of recursive definitions each with an initial condition: a j − 1 = e − 1 a j a l −
Symmetric level-index arithmetic
Symmetric_level-index_arithmetic
Pattern in mathematics and computer science
{\displaystyle \Delta =\{x_{1},x_{2},...\}} , Zimin words (patterns) are defined recursively Z n + 1 = Z n x n + 1 Z n {\displaystyle Z_{n+1}=Z_{n}x_{n+1}Z_{n}} for
Unavoidable_pattern
Concept in computability theory
{\displaystyle T_{1}} predicate is primitive recursive in the sense that there is a primitive recursive function that, given inputs for the predicate
Kleene's_T_predicate
Discrete Fourier transform for prime sizes
savings for the case of DFTs of real data, using a slightly modified re-indexing/permutation to obtain two half-size cyclic convolutions of real data; an
Rader's_FFT_algorithm
Specification in economics of recursive utility
economics, Epstein–Zin preferences refers to a specification of recursive utility. A recursive utility function can be constructed from two components,: a
Epstein–Zin_preferences
Finite or infinite ordered list of elements
±1-sequence Arithmetic progression Automatic sequence Cauchy sequence Constant-recursive sequence Geometric progression Harmonic progression Holonomic sequence
Sequence
Finite-state machine
function composition. Clearly, this process may be recursively continued, giving the following recursive definition of δ ^ : Q × Σ ⋆ → Q {\displaystyle {\widehat
Deterministic finite automaton
Deterministic_finite_automaton
Lemma that defines a property of regular languages
concatenation Indexed — Linear context-free rewriting systems Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular — Non-recursive Recursively
Pumping lemma for regular languages
Pumping_lemma_for_regular_languages
Fast approximate median algorithm
median of medians algorithm guarantees a worst-case runtime of O(n) by recursively selecting good pivot elements, discarding at least 30% of elements at
Median_of_medians
Programming language with hardware abstraction
supports constructs such as expression evaluation, parameterized and recursive functions, data types and structures which are generally not supported
High-level programming language
High-level_programming_language
Index of articles associated with the same name
240–284. doi:10.1090/s0002-9904-1969-12138-5. ISSN 0273-0979. This set index article includes a list of related items that share the same name (or similar
Stratification_(mathematics)
Metric of academic journals
diamScore – a measure of scientific influence of academic journals based on recursive citation weighting and the pairwise comparisons between journals. Source
Journal_ranking
Divide and conquer sorting algorithm
Example C-like code using indices for top-down merge sort algorithm that recursively splits the list into sublists (called runs in this example) until sublist
Merge_sort
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