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A simple base case (or cases) — a terminating scenario that does not use recursion to produce an 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 person's ancestor. One's ancestor is either: One's parent (base case), or
where a represents the number of recursive calls at each level of recursion, b represents by what factor smaller the input is for the next level of recursion (i.e. the number of pieces you divide the problem into), and f(n) represents the work that the function does independently of any recursion (e.g. partitioning, recombining) at each level ...
The μ-recursive functions (or general recursive functions) are partial functions that take finite tuples of natural numbers and return a single natural number.They are the smallest class of partial functions that includes the initial functions and is closed under composition, primitive recursion, and the minimization operator μ.
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
Most recursive definitions have two foundations: a base case (basis) and an inductive clause. The difference between a circular definition and a recursive definition is that a recursive definition must always have base cases, cases that satisfy the definition without being defined in terms of the definition itself, and that all other instances in the inductive clauses must be "smaller" in some ...
In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language.
In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventually lead to a string that includes the same non-terminal again.
In the following, the abbreviation x = def x 1, ... x n; subscripts may be applied if the meaning requires. #A: A function φ definable explicitly from functions Ψ and constants q 1, ... q n is primitive recursive in Ψ. #B: The finite sum Σ y<z ψ(x, y) and product Π y<z ψ(x, y) are primitive recursive in ψ.