Examples of using Computable function in English and their translations into Portuguese
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Every computable function is arithmetically definable.
Let F be a prefix-free universal computable function.
Thus given a set formula_5, a computable function formula_6 has property"F" if and only if formula_7.
Denote by formula_3 the th(partial) computable function.
Each computable function has an infinite number of different program representations in a given programming language.
This argument provides a total computable function that is not primitive recursive.
Definition==Let"P"F be the domain of a prefix-free universal computable function"F.
Thus every computable function must have a finite program that completely describes how the function is to be computed.
This means that"F" can be used to simulate any computable function of one variable.
If"g" were a total computable function extending"f" then"g" would be computable by some Turing machine; fix"e" as the index of such a machine.
Let formula_2 be an index of the composition formula_34,which is a total computable function.
Blum's speedup theorem, which provides speedup by any computable function not just linear, as in the previous theorem.
Thus a set is computably enumerable if andonly if it is the domain of some computable function.
It is not a computable number;there is no computable function that enumerates its binary expansion, as discussed below.
Let e{\displaystyle e} be an index of thecomposition F∘ h{\displaystyle F\circ h}, which is a total computable function.
Goodstein's theorem can be used to construct a total computable function that Peano arithmetic cannot prove to be total.
This means that any function computable from the path is dominated by a computable function.
Every Turing machine computes a certain fixed partial computable function from the input strings over its alphabet.
The definition of a halting probability relies on the existence of a prefix-free universal computable function.
Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set.
Equivalently, a set is recursively enumerable if andonly if it is the range of some computable function.
If formula_58 is a recursive set,then for some formula_16, computable function formula_6is the characteristic function of formula_58.
If the fundamental sequences are computable(e.g., as in the Wainer hierarchy),then every fα is a total computable function.
The preimage of a recursive set under a total computable function is a recursive set.
Equivalently, a weak truth-table reduction is a Turing reduction for which the use of the reduction is bounded by a computable function.
Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set see undecidable problem.
Limitations==Primitive recursive functions tend to correspond very closely with our intuition of what a computable function must be.
For any recursive operator Ψ there is a partial computable function φ such that Ψ(φ) φ and φ is the smallest partial computable function with this property.
The image of a computable set under a nondecreasing total computable function is computable. .
We write formula_5 for the"i"-th partial computable function under the Gödel numbering formula_2, andformula_7 for the partial computable function formula_8.