Rekursiivne

Rekursiivne is an adjective used to describe processes, definitions or structures that refer to themselves or are defined in terms of their own previous state. In many disciplines it denotes a self-referential or self-similar pattern that unfolds by repeating a similar operation on smaller or simpler instances.

In mathematics and computer science rekursiivne often refers to recursive definitions and recursive algorithms. A recursive definition specifies an object in terms of a smaller instance of itself, together with one or more base cases that stop the recursion. Common examples include the factorial function, defined by n! = n · (n−1)! with 0! = 1, and the Fibonacci sequence, defined by F(n) = F(n−1) + F(n−2) with F(0) and F(1) as base values. In programming, rekursiivne functions call themselves with updated arguments until a base case is reached; this technique is frequently used in tree or graph traversal, sorting, and parsing tasks.

In linguistics, rekursiivne describes recursive structures where phrases are embedded within phrases of the same type, allowing potentially unbounded sentence expansion. This concept is central to theories of language hierarchy and syntax, though its empirical status is debated in some linguistic traditions.

A practical caveat is that poorly designed recursion can lead to infinite recursion and program crashes, hence termination conditions and, in some cases, tail recursion optimization are important considerations. The term is closely related to rekursioon, referring to the broader idea of self-reference across disciplines.