primitive recursive functions
[prɪˈmɪtɪv rɪˈkɜːrsɪv ˈfʌŋkʃənz]
noun
funções recursivas primitivas
1. A class of mathematical functions computable by algorithms that use only basic operations (zero, successor, and projection) and composition and primitive recursion, excluding unbounded search
Addition and multiplication are examples of primitive recursive functions.
Adição e multiplicação são exemplos de funções recursivas primitivas.
2. Functions that can be defined through a finite sequence of steps without requiring general recursion or iteration with unknown termination
The Ackermann function is not primitive recursive because it requires a more powerful form of recursion.
A função de Ackermann não é recursiva primitiva porque requer uma forma mais poderosa de recursão.
3. A subset of total computable functions that are guaranteed to terminate in finite time
All primitive recursive functions are total functions that always produce an output.
Todas as funções recursivas primitivas são funções totais que sempre produzem uma saída.
This is a specialized term from mathematical logic and theoretical computer science with no cultural variation. It is used identically in academic settings across Brazil, Portugal, and English-speaking countries. The concept is central to understanding computational limits and the Church-Turing thesis in computer science curricula.
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