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A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length n X (often much longer than the length of X) such that X appears in every block of length n X. [1] [6] [7] The terms minimal sequence [8] and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.
In mathematics, recurrent sequence may refer to: A sequence satisfying a recurrence relation Recurrent word , a sequence such that any factor (consecutive subsequence) that appears does so infinitely often, such as the Thue–Morse sequence or a Sturmian word
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
A sequence obeying the order-d equation also obeys all higher order equations. These identities may be proved in a number of ways, including via the theory of finite differences. [9] Any sequence of + integer, real, or complex values can be used as initial conditions for a constant-recursive sequence of order +.
Recursive definition; Recurrent neural network, a special artificial neural network; Recurrence period density entropy, an information-theoretic method for summarising the recurrence properties of dynamical systems; Recurrence plot, a statistical plot that shows a pattern that re-occurs; Recurrence relation, an equation which defines a sequence ...
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. [1] Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition ...
A sequence of idempotent subroutines where at least one subroutine is different from the others, however, is not necessarily idempotent if a later subroutine in the sequence changes a value that an earlier subroutine depends on—idempotence is not closed under sequential composition. For example, suppose the initial value of a variable is 3 ...