computation that has ever been imagined can compute only computable functions, and all computable functions can be computed by any of several models of computation...

the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel...

with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability...

exponential function, and the function which returns the nth prime are all primitive recursive. In fact, for showing that a computable function is primitive...

pairing function) are computably enumerable sets. The preimage of a computably enumerable set under a partial computable function is a computably enumerable...

{\displaystyle S} of the natural numbers is called computable if there exists a total computable function f {\displaystyle f} such that f ( x ) = 1 {\displaystyle...

total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates...

recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in...

"On Non-Computable Functions". One of the most interesting aspects of the busy beaver game is that, if it were possible to compute the functions Σ(n) and...

function may refer to: Recursive function (programming), a function which references itself General recursive function, a computable partial function...

computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in...

Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in...

often in discussions of computability since it demonstrates that some functions are mathematically definable but not computable. A key part of the formal...

ideas leads to the author's definition of a computable function, and to an identification of computability with effective calculability. It is not difficult...

μ-recursive function, defined from a particular formal model of computable functions using primitive recursion and the μ operator Computable function, or total...

of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by...

In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions...

partial function computable by a partial Turing machine be extended (that is, have its domain enlarged) to become a total computable function? Is it possible...

recognize. The domain of any universal computable function is a computably enumerable set but never a computable set. The domain is always Turing equivalent...

acceptable definition of a computable function defines also the same functions. General recursive functions are partial functions from integers to integers...

In computer science, Programming Computable Functions (PCF) is a typed functional language introduced by Gordon Plotkin in 1977, based on previous unpublished...

that not every function is computable. Every computable real function is continuous. The arithmetic operations on real numbers are computable. While the equality...

a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computable in the Church–Turing sense. Technically...

arbitrary function with domain ω and only countably many computable functions. A specific example of a set with an enumeration but not a computable enumeration...

numbering of the computable functions in terms of the smn theorem and the UTM theorem. The theorem states that a partial computable function u of two variables...

total computable functions such that the index set of P is decidable with a promise that the input is the index of a total computable function (i.e.,...

Turing-equivalent if every function it can compute is also Turing-computable; i.e., it computes precisely the same class of functions as do Turing machines...

computability theory, a function f : R → R {\displaystyle f\colon \mathbb {R} \to \mathbb {R} } is sequentially computable if, for every computable sequence...

computational complexity theory, the complexity class FL is the set of function problems which can be solved by a deterministic Turing machine in a logarithmic...

In computer science, a universal function is a computable function capable of calculating any other computable function. It is shown to exist by the utm...