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Let G be a finite group and let S be a subset of G.A straight-line program of length m over S computing some g ∈ G is a sequence of expressions (w 1,...,w m) such that for each i, w i is a symbol for some element of S, or w i = (w j,-1) for some j < i, or w i = (w j,w k) for some j,k < i, such that w m takes upon the value g when evaluated in G in the obvious manner.
a finite procedure, written in a fixed symbolic vocabulary, governed by precise instructions, moving in discrete steps, 1, 2, 3, . . ., whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end." (boldface and italics in the original, p. xviii)
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special solution if a simple graph for the given degree sequence ...
An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type ...
The Fisher–Yates shuffle is an algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and continually determines the next element in the shuffled sequence by randomly drawing an element from the list until no elements remain. [ 1 ]
As there are only a finite number of possible n-tuples with these constraints, the sequence of n-tuples must sooner or later repeat itself. Every Ducci sequence therefore eventually becomes periodic. If n is a power of 2 every Ducci sequence eventually reaches the n-tuple (0,0,...,0) in a finite number of steps. [1] [3] [4]
The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S 0, S 1, and S 2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1.