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...

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

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

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], ...

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...

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...

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

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...

_{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...

_{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...

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

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], ...

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...

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

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...

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...

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

"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...

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...

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

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}...

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

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

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...

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...