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...

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

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

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...

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

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 triple (L, S, R), where...

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...

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

"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...

X_{n})} . Sometimes the notation σk is used instead of ek. The following definition is equivalent to the above and might be useful for computer implementations:...

numbers that is more efficient than the one given by their original recursive definition: ( m + 3 m ) B m = { m + 3 3 − ∑ j = 1 m 6 ( m + 3 m − 6 j ) B m...

_{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...

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...

_{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...

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...

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], ...

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

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...

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

somewhat different definitions of the so-called associated Laguerre polynomials.) One can also define the Laguerre polynomials recursively, defining the first...

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

programming practical recursive functions are needed. A central property of the lambda calculus is that recursive definitions are not directly available...

examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function...

also maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree. One way to define the question-mark...

notion of computability available at the time. Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal...

A recursive acronym is an acronym that refers to itself, and appears most frequently in computer programming. The term was first used in print in 1979...

definitions. The class of computable functions can be defined in many equivalent models of computation, including Turing machines General recursive functions...

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