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Binary sequence
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free
Algorithmically random sequence
Algorithmically_random_sequence
Subfield of information theory and computer science
example, it is an algorithmically random sequence and thus its binary digits are evenly distributed (in fact it is normal). Algorithmic information theory
Algorithmic information theory
Algorithmic_information_theory
Sequence of random variables
concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables
Random_sequence
Number generated by a random process
needed] Algorithmically random sequence Quasi-random sequence Random number generation Non-uniform random number generation Random real Random sequence Random
Random_number
Halting probability of a random computer program
enumerated. A real number is random if the binary sequence representing the real number is an algorithmically random sequence. Calude, Hertling, Khoussainov
Chaitin's_constant
Type of mathematical sequence
values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties of random variables and in certain applications
Low-discrepancy_sequence
Algorithm that generates an approximation of a random number sequence
random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers
Pseudorandom_number_generator
Computer science professor
theory of algorithmic randomness. He co-authored a paper demonstrating that a recursively enumerable real number is an algorithmically random sequence if and
Yongge_Wang
Creating sequence of numbers that cannot be predicted
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that
Random_number_generation
optimization algorithm Odds algorithm (Bruss algorithm): Finds the optimal strategy to predict a last specific event in a random sequence event Random Search
List_of_algorithms
Apparent lack of pattern or predictability in events
In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols
Randomness
Algorithm for shuffling a finite sequence
next element in the shuffled sequence by randomly drawing an element from the list until no elements remain. The algorithm produces an unbiased permutation:
Fisher–Yates_shuffle
Data evaluation test
NIST Statistical Test Suite Randomness Statistical randomness Algorithmically random sequence Seven states of randomness Wald–Wolfowitz runs test Wolfram
Randomness_test
Algorithm that arranges lists in order
some algorithms are designed for sequential access, the highest-performing algorithms assume data is stored in a data structure which allows random access
Sorting_algorithm
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution
Convergence of random variables
Convergence_of_random_variables
Sequence of operations for a task
each step, eventually producing output and terminating. Randomized algorithms incorporate random inputs which can be used to simulate non-deterministic
Algorithm
Appearing random but actually being generated by a deterministic, causal process
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable
Pseudorandomness
Value used to initialize a pseudo-random number generator
will produce the same sequence of numbers. For a seed to be used in a pseudorandom number generator, it does not need to be random. Because of the nature
Random_seed
Seemingly random, difficult to predict bit stream created by a deterministic algorithm
difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information
Pseudorandom_binary_sequence
German mathematician and cryptographer (1943–2025)
approach to the definition of an algorithmically random sequence which is alternative to the concept of Martin-Löf randomness. Schnorr was a professor of mathematics
Claus_P._Schnorr
Type of numeric sequence used in statistics
is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalize the
Halton_sequence
Sequence where any order is equally likely
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a
Random_permutation
Algorithm for generating pseudo-randomized numbers
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear
Linear_congruential_generator
Automated method for solving mazes
maze-solving algorithm is an automated method for solving a maze. The random mouse, wall follower, Pledge, Tarry's, and Trémaux's algorithms are designed
Maze-solving_algorithm
Method in which data is created algorithmically as opposed to manually
of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated
Procedural_generation
Swedish logician, philosopher, and mathematical statistician
invariant to the model of computation being used. An algorithmically random sequence is an infinite sequence of characters, all of whose prefixes (except possibly
Per_Martin-Löf
Lossless data compression algorithms
non-random nature of a sequence. The algorithms represent the dictionary as an n-ary tree, where n is the number of tokens used to form token sequences.
LZ77_and_LZ78
Cryptographic device
number generator (PRNG) that utilizes a deterministic algorithm and non-physical nondeterministic random bit generators that do not include hardware dedicated
Hardware random number generator
Hardware_random_number_generator
Low-space search for a majority element
The Boyer–Moore majority vote algorithm is an algorithm for finding the majority of a sequence of elements using linear time and a constant number of words
Boyer–Moore majority vote algorithm
Boyer–Moore_majority_vote_algorithm
Measure of algorithmic complexity
randomness for infinite sequences from a finite alphabet. These algorithmically random sequences can be defined in three equivalent ways. One way uses an effective
Kolmogorov_complexity
Algorithm in numerical analysis
summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision
Kahan_summation_algorithm
Tree-based ensemble machine learning methods
their training set. The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's
Random_forest
Type of algorithm in computer science
passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the
Deterministic_algorithm
Software library for the C++ programming language
feature that allow the generality of the STL. For example, an algorithm to reverse a sequence can be implemented using bidirectional iterators, and then
Standard_Template_Library
Algorithm for determining similar regions between two molecular sequences
Smith–Waterman algorithm performs local sequence alignment; that is, for determining similar regions between two strings of nucleic acid sequences or protein
Smith–Waterman_algorithm
Cycle through all length-k sequences
The Logic of Scientific Discovery (1934), calling them "shortest random-like sequences". Taking A = {0, 1}, there are two distinct B(2, 3): 00010111 and
De_Bruijn_sequence
Class of statistical modeling methods
In pattern recognition and machine learning, conditional random field (CRF) is a class of statistical modeling methods often used for structured prediction
Conditional_random_field
Overview of and topical guide to computer programming
algorithms Empirical algorithmics Big O notation Algorithmic efficiency Algorithmic information theory Algorithmic probability Algorithmically random
Outline of computer programming
Outline_of_computer_programming
Numbers obtained by adding the two previous ones
word – Binary sequence from Fibonacci recurrence Random Fibonacci sequence – Randomized mathematical sequence based upon the Fibonacci sequence Wythoff array –
Fibonacci_sequence
Number with all digits equally frequent
appear random to any finite-state machine. Compare this with the algorithmically random sequences, which are those infinite sequences that appear random to
Normal_number
Monte Carlo algorithm
physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution
Metropolis–Hastings_algorithm
On finding a repeating loop in a sequence
science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function f that
Cycle_detection
Type of sequence in numerical analysis
Sobol' sequences (also called LPτ sequences or (t, s) sequences in base 2) are a type of quasi-random low-discrepancy sequence. They were first introduced
Sobol_sequence
Process of making something random
Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing
Randomization
Statistical Markov model
that room and randomly draws a ball from that urn. It then puts the ball onto a conveyor belt, where the observer can observe the sequence of the balls
Hidden_Markov_model
Quality of a numerical sequence of having no recognizable patterns
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal
Statistical_randomness
Discrete Fourier transform algorithm
Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts
Fast_Fourier_transform
Nucleotide or amino-acid sequence pattern
In biology, a sequence motif is a nucleotide or amino-acid sequence pattern that is widespread and usually assumed to be related to biological function
Sequence_motif
Divide-and-conquer algorithm for generating a random permutation of a finite set
a divide-and-conquer algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and for each element
Rao–Sandelius_shuffle
Type of functions designed for being unsolvable by root-finding algorithms
pass statistical randomness tests: Every CSPRNG should satisfy the next-bit test. That is, given the first k bits of a random sequence, there is no polynomial-time
Cryptographically secure pseudorandom number generator
Cryptographically_secure_pseudorandom_number_generator
Art genre
can be introduced by using pseudo-random numbers. There is no consensus as to whether the product of an algorithm that operates on an existing image
Algorithmic_art
Random process of binary (boolean) random variables
process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes
Bernoulli_process
Overview of and topical guide to algorithms
to algorithms: An algorithm is a finite, well-defined sequence of instructions or rules for solving a problem or performing a computation. Algorithms are
Outline_of_algorithms
Sorting algorithm
behavior is to consider the probability of obtaining a sorted sequence after repeated random shuffles. This is analogous to the general formula for the probability
Bogosort
Form of computer memory
Random-access memory (RAM; /ræm/) is a form of electronic computer memory that can be read and changed in any order, typically used to store working data
Random-access_memory
Process forming a path from many random steps
\{S_{n}\}} is called the simple random walk on Z {\displaystyle \mathbb {Z} } . This series (the sum of the sequence of −1s and 1s) gives the net distance
Random_walk
Online database of integer sequences
large number of different algorithms to identify sequences related to the input. Neil Sloane started collecting integer sequences as a graduate student in
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
language • Alex Biryukov • Alfred Menezes • Algebraic Eraser • Algorithmically random sequence • Alice and Bob • All-or-nothing transform • Alphabetum Kaldeorum
Index of cryptography articles
Index_of_cryptography_articles
Equivalence of average-case and expected complexity
the performance of randomized algorithms to deterministic (non-random) algorithms. It states that, for certain classes of algorithms, and certain measures
Yao's_principle
Computer memory concept
Random access (also called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of
Random_access
Iterative algorithm on numbers
is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a four-digit random number, sorts the
Kaprekar's_routine
Computational concept
unbiasing algorithms, as they take the randomness from a so-called "biased" source and output a distribution that appears unbiased. The weakly random source
Randomness_extractor
Finds likely sequence of hidden states
The Viterbi algorithm is a dynamic programming algorithm that finds the most likely sequence of hidden events that would explain a sequence of observed
Viterbi_algorithm
Software testing technique that tests programs with random inputs
probability of failure is less than 1/100. Random input sequence generation (i.e. a sequence of method calls) Random sequence of data inputs (sometimes called stochastic
Random_testing
Sequence in computer science
output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting
Prefix_sum
Counterintuitive result in probability
monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. Variants of the theorem include multiple and
Infinite_monkey_theorem
Mathematical method of assigning a prior probability to a given observation
motivated by information theory and problems in randomness, while Solomonoff introduced algorithmic complexity for a different reason: inductive reasoning
Algorithmic_probability
128-bit number used to identify information in computer systems
end of the key sequence, and records which are close in time are near each other in the key sequence. This contrasts with the random version 4, which
Universally_unique_identifier
Class of algorithms operating on data streams
streaming algorithms process input data streams as a sequence of items, typically making just one pass (or a few passes) through the data. These algorithms are
Streaming_algorithm
Numerical optimization method
Chen/jcfit: A Random Search Algorithm for general mathematical model(s) fittings". GitHub. Rastrigin, L.A. (1963). "The convergence of the random search method
Random_search
theoretic method for proving that a random process terminates, originally used by Robin Moser to prove an algorithmic version of the Lovász local lemma
Entropy_compression
Algorithmic problem on pairs of sequences
(LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring:
Longest_common_subsequence
Scale-free network generation algorithm
The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and
Barabási–Albert_model
do not rely on cipher algorithms but try to link mathematically the difficulty of distinguishing their output from a `true' random stream to a computationally
List of random number generators
List_of_random_number_generators
Field of machine learning
action-value function are value iteration and policy iteration. Both algorithms compute a sequence of functions Q k {\displaystyle Q_{k}} ( k = 0 , 1 , 2 , … {\displaystyle
Reinforcement_learning
Divide and conquer sorting algorithm
merge sort and heapsort for randomized data, particularly on larger distributions. Quicksort is a divide-and-conquer algorithm. It works by selecting a "pivot"
Quicksort
Algorithm used for pathfinding and graph traversal
heuristic. The algorithm described so far only gives the length of the shortest path. To find the actual sequence of steps, the algorithm can be easily
A*_search_algorithm
Algorithm for caching data
Bélády's algorithm cannot be implemented there. Random replacement selects an item and discards it to make space when necessary. This algorithm does not
Cache_replacement_policies
Random search tree data structure
any sequence of insertions and deletions of keys, the shape of the tree is a random variable with the same probability distribution as a random binary
Treap
Algorithm in mathematics
modeling of genomic sequences. A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It
Baum–Welch_algorithm
Statistical tool to model changing systems
corresponding sequence of states, the forward algorithm will compute the probability of the sequence of observations, and the Baum–Welch algorithm will estimate
Markov_model
Binary tree derived from a sequence of numbers
nearly-sorted inputs, and as the basis for pattern matching algorithms. A Cartesian tree for a sequence can be constructed in linear time. Cartesian trees are
Cartesian_tree
Materials science algorithm
The rainflow-counting algorithm is used in calculating the fatigue life of a component in order to convert a loading sequence of varying stress into a
Rainflow-counting_algorithm
Stream cipher
algorithm has also been attacked, with Alexander Maximov and a team from NEC developing ways to distinguish its output from a truly random sequence.
RC4
Algorithm to be run on quantum computers
circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem
Quantum_algorithm
Numerical integration process
some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. This is
Quasi-Monte_Carlo_method
Family of iterative methods
without evaluating it directly. Instead, stochastic approximation algorithms use random samples of F ( θ , ξ ) {\textstyle F(\theta ,\xi )} to efficiently
Stochastic_approximation
Supervised machine learning techniques
can be exploited in a sequence model such as a hidden Markov model or conditional random field that predicts the entire tag sequence for a sentence (rather
Structured_prediction
Graph generated by a random process
context of random graphs refers to a sequence of spaces and probabilities, such that the error probabilities tend to zero. The theory of random graphs studies
Random_graph
the deterministic algorithm on their own to precompute the most disastrous sequence. Consider the following simple randomized algorithm : BIT For every
List_update_problem
Algorithmic technique
was in an algorithm named "fictitious play" which was proposed in game theory in the early 1950s. Grigoriadis and Khachiyan applied a randomized variant
Multiplicative weight update method
Multiplicative_weight_update_method
Probabilistic problem-solving algorithm
Monte Carlo simulations, are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results, conceptualized
Monte_Carlo_method
Subset of artificial intelligence
such as images, video, and sensory data have not yielded attempts to algorithmically define specific features. An alternative is to discover such features
Machine_learning
Computer science problem
context of various disciplines related to mathematics, including algorithmics, random matrix theory, representation theory, and physics. The longest increasing
Longest increasing subsequence
Longest_increasing_subsequence
Binary tree selected at random
operations that maintain this random structure even when the update sequence is non-random. Other distributions on random binary trees include the uniform
Random_binary_tree
Divide and conquer sorting algorithm
merge algorithm. Cormen et al. present a binary variant that merges two sorted sub-sequences into one sorted output sequence. In one of the sequences (the
Merge_sort
Method of computing optimal strategies for last-success problems
than all preceding bids, and coded 0 otherwise. The bids will form a random sequence of 0s and 1s. Only 1s interest the seller, who may fear that each successive
Odds_algorithm
Procedure used to randomize a deck of playing cards
simulated using algorithms like the Fisher–Yates shuffle, which generates a random permutation of cards. In online gambling, the randomness of shuffling
Shuffling
Automated recognition of patterns and regularities in data
(meta-algorithm) Bootstrap aggregating ("bagging") Ensemble averaging Mixture of experts, hierarchical mixture of experts Bayesian networks Markov random fields
Pattern_recognition
Open problem on 3x+1 and x/2 functions
Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable. Specifically, he considered functions of the form g (
Collatz_conjecture
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ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Boy/Male
English American
Son of Rand.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Boy/Male
English
Son of Rand.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : variant of Brandon.
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Surname or Lastname
English
English : patronymic from Rand 1.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Surname or Lastname
English
English : variant of Ransom.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
ALGORITHMICALLY RANDOM-SEQUENCE
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