In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements...

answer A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that...

noted that some definitions are "legal" or "coercive" – their object is to create or alter rights, duties, or crimes. A recursive definition, sometimes also...

target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end...

two types. This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest: t: v [t[1], ...

functional programming languages and provide a means to allow for recursive definitions. In the classical untyped lambda calculus, every function has a...

aspects Mathematics: Intensional definition Elementary definition Algebraic definition Recursive definition Field of definition A continuous function A well-defined...

self-referential definition. There are two types of self-referential definitions: inductive and coinductive definitions. An inductively defined recursive data definition...

Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost...

_{2}+\mathbf {P} _{1})\,.} Bézier curves can be defined for any degree n. A recursive definition for the Bézier curve of degree n expresses it as a point-to-point...

child and the right child. That is, it is a k-ary tree with k = 2. A recursive definition using set theory is that a binary tree is a tuple (L, S, R), where...

_{k=0}^{n}{\binom {n}{k}}} If S is a finite set, then a recursive definition of P(S) proceeds as follows: If S = {}, then P(S) = { {} }. Otherwise...

entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the...

Pfaffian of a skew-symmetric 2n × 2n matrix A with n > 0 can be computed recursively as pf ⁡ ( A ) = ∑ j = 1 j ≠ i 2 n ( − 1 ) i + j + 1 + θ ( i − j ) a i...

of the equivalence of the four approaches. The following is the recursive definition for the Bernoulli numbers: B m + = − 1 m + 1 ∑ k = 0 m − 1 ( m +...

machines, register machines, lambda calculus and general recursive functions. Before the precise definition of computable function, mathematicians often used...

factorial values for increasing numbers 1, 2, 3... as in the above recursive definition with "time arrow" reversed, as it were, by reading it backwards as...

the children. This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest: t: v [t[1], ...

defined via recursive definitions. The statement of the theorems refers to an admissible numbering φ {\displaystyle \varphi } of the partial recursive functions...

interpret its own construction, so that this construction is non-recursive (as recursive definitions would be unambiguous). Also, if T {\displaystyle T} is at...

6-LUT, hence an entire ALM. An open-source Verilog generator for the recursive priority-encoder is available online. A behavioral description of priority...

"multidigraph". In a correspondence to the types of entities used in the recursive definition, each node of an apq is assigned a type (1), (2a), (2b), (2c) or...

There are two equivalent major definitions for the concept of a recursive language: A recursive formal language is a recursive subset in the set of all possible...

few Laguerre polynomials: One can also define the Laguerre polynomials recursively, defining the first two polynomials as L 0 ( x ) = 1 {\displaystyle L_{0}(x)=1}...

into the definition of the rank of a set gives a self-contained recursive definition: The rank of a set is the smallest ordinal number strictly greater...

artery – arising from the radial artery immediately below the elbow Recursive definition Recurrent neural network, a special artificial neural network Recurrence...

}}n>0\end{cases}}} The recursive definition is equivalent to repeated exponentiation for natural heights; however, this definition allows for extensions...

Self-reference Self-refuting idea Recursive definition Revision theory Tautology Vicious circle principle "Circular Definition". Glossary of Linguistic Terms...