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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.
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
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 ...
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 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]
The following result is a generalisation of the monotone convergence of non negative sums theorem above to the measure theoretic setting. It is a cornerstone of measure and integration theory with many applications and has Fatou's lemma and the dominated convergence theorem as direct consequence.
A finite sequence must terminate with a state. An execution is defined as an execution fragment that begins with start state. The set of executions of A is represented by execs(A). A reachable state in I/O automaton A is the final state of a finite execution of A. Assume α is a finite execution fragment of A ending with state s f.
A termination proof is a type of mathematical proof that plays a critical role in formal verification because total correctness of an algorithm depends on termination.. A simple, general method for constructing termination proofs involves associating a measure with each step of an algorithm.