This article is about iterated functions. For another use, see Cycle detection (graph theory).
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In computer 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 maps a finite set S to itself, and any initial value x0 in S, the sequence of iterated function values
must eventually use the same value twice: there must be some pair of distinct indices i and j such that xi = xj. Once this happens, the sequence must continue periodically, by repeating the same sequence of values from xi to xj − 1. Cycle detection is the problem of finding i and j, given f and x0.
Several algorithms are known for finding cycles quickly and with little memory. Robert W. Floyd's tortoise and hare algorithm moves two pointers at different speeds through the sequence of values until they both point to equal values. Alternatively, Brent's algorithm is based on the idea of exponential search. Both Floyd's and Brent's algorithms use only a constant number of memory cells, and take a number of function evaluations that is proportional to the distance from the start of the sequence to the first repetition. Several other algorithms trade off larger amounts of memory for fewer function evaluations.
The applications of cycle detection include testing the quality of pseudorandom number generators and cryptographic hash functions, computational number theory algorithms, detection of infinite loops in computer programs and periodic configurations in cellular automata, automated shape analysis of linked list data structures, and detection of deadlocks for transactions management in DBMS.
In computer science, cycledetection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any...
Cherkassky and Goldberg survey several other algorithms for negative cycledetection. Many problems can be framed as a form of the shortest path for some...
repeating values Cycledetection, the algorithmic problem of detecting repetitions in sequences generated by iterated functions Cycle, a set equipped with...
image-to-image translation approach, such as cycle-GAN. Among other uses, cross-domain object detection is applied in autonomous driving, where models...
Python also uses reference counting and offers cycledetection as well (and can reclaim reference cycles). Like other low-level languages, Rust does not...
cycleCycle graph, a graph that has the structure of a single cycle Pancyclic graph, a graph that has cycles of all possible lengths Cycledetection (graph...
collision warning with automatic braking, lane-keep assist, pedestrian/cycledetection, active lane management, blind-spot monitor, and rear cross-traffic...
A detection dog or sniffer dog is a dog that is trained to use its senses to detect substances such as explosives, illegal drugs, wildlife scat, currency...
algorithms are also capable of detecting cycles in their inputs; however, it may be desirable to perform cycledetection separately from topological sorting...
development. Buffalo have an estrous cycle of about 22 to 24 days. Buffalo are known for difficult estrus detection. This is one major reason for being...
any particular n, the Pisano period may be found as an instance of cycledetection. The Fibonacci sequence is one of the simplest and earliest known sequences...
the cycle repeats and allows the system to automatically recognize new unforeseen patterns in the network. This system can average 99.9% detection and...
The menstrual cycle is a series of natural changes in hormone production and the structures of the uterus and ovaries of the female reproductive system...
finite dimensions. Wikimedia Commons has media related to Attractor. Cycledetection Hyperbolic set Stable manifold Steady state Wada basin Hidden oscillation...
Meteorological Service of Canada, the European Cooperation for Lightning Detection (EUCLID), the Institute for Ubiquitous Meteorology (Ubimet) and by other...
The cell cycle, or cell-division cycle, is the series of events that take place in a cell that causes it to divide into two daughter cells. These events...
late 1930s. The first reports of the experimental detection of the neutrinos produced by the CNO cycle in the Sun were published in 2020 by the BOREXINO...
disabling the entire program whenever the box came up. Mathematics portal Cycledetection Divergence (computer science) Fork bomb (an infinite loop is one of...
use standard fieldbus cables and messages. They do not depend on error detection mechanisms of underlying transmission channels, and thus supports securing...
multiple cycles of PCR produces inaccurate end point quantification due to the difficulty in maintaining linearity. In order to provide accurate detection and...
respectively, in the Phage Discovery Guide. Detection methods of phages released from the lysogenic cycle include electron microscopy, DNA extraction...
not as accurate or as sensitive as the nucleic acid detection methods. The exact replication cycle of sapovirus has not been determined; however, it is...
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