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In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion ...
The rule for generating new functions by recursion is F(z, x) = G(∪ u ∈ z F(u, x), z, x) A primitive recursive ordinal function is defined in the same way, except that the initial function F(x, y) = x ∪ {y} is replaced by F(x) = x ∪ {x} (the successor of x). The primitive recursive ordinal functions are the same as the primitive ...
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 ...
An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i ...
This branch of computability theory analyzed the following question: For fixed m and n with 0 < m < n, for which functions A is it possible to compute for any different n inputs x 1, x 2, ..., x n a tuple of n numbers y 1, y 2, ..., y n such that at least m of the equations A(x k) = y k are true. Such sets are known as (m, n)-recursive sets.
In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. [1] Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers , where the datatypes are ...
For instance, the most common characterization of the primitive recursive functions is as the 0 constant and successor function closed under projection, composition and primitive recursion. So for a (n+1)-place function f defined by primitive recursion over a n-place base function g and (n+2)-place iteration function h there would be the ...
This strategy avoids the overhead of recursive calls that do little or no work and may also allow the use of specialized non-recursive algorithms that, for those base cases, are more efficient than explicit recursion. A general procedure for a simple hybrid recursive algorithm is short-circuiting the base case, also known as arm's-length ...