General recursive function

In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function

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enIn mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function
Has abstract
enIn mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the functions of lambda calculus and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.
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General recursive function
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enGeneral recursive function
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books.google.com/books%3Fid=0LpsXQV2kXAC&pg=PA70
books.google.com/books%3Fid=9I7Pl00LU5gC&pg=PP1
people.irisa.fr/Francois.Schwarzentruber/recursive_functions_to_turing_machines/
plato.stanford.edu/entries/recursive-functions/
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Ackermann function
Category:Computability theory
Category:Theory of computation
Church's thesis
Church–Turing thesis
Computability theory (computation)
Computable function
Computational complexity theory
Computer science
Domain of a function
Fibonacci number
Halting problem
Integer square root
Journal of Symbolic Logic
Junctor
Kleene's T predicate
Lambda calculus
Logical negation
Markov algorithm
Marvin Minsky
Mathematical logic
McCarthy 91 function
Natural number
Partial function
Primitive recursive function
Primitive recursive functions
R (complexity)
Recursion
Recursion (computer science)
Recursion theory
Register machine
Total Turing machine
Turing machine
Universal Turing machine
Μ operator
P
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1
3
7
SameAs
2eRBh
Částečně rekurzivní funkce
Fonction récursive
Função μ-recursiva
Función recursiva
Funció recursiva
Funkcja rekurencyjna
Funzione ricorsiva
Q284164
Μ-recursieve functie
Μ-Rekursion
Μ-αναδρομική συνάρτηση
Μ-рекурзивна функција
Μ再帰関数
Μ-재귀 함수
פונקציה רקורסיבית
تابع μ-بازگشتی
递归函数
Subject
Category:Computability theory
Category:Theory of computation
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Рекурсивная функция (теория вычислимости)
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