Exemplos de uso de Total computable em Inglês e suas traduções para o Português
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Is the range of a total computable function.
Let formula_2 be an index of the composition formula_34,which is a total computable function.
This argument provides a total computable function that is not primitive recursive.
In this dissertation an intentional andextensional study of the class of total computable functions is made.
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.
R is equal to the set of all total computable functions.
Not every total computable function is provably total in Peano arithmetic, however; an example of such a function is provided by Goodstein's theorem.
The preimage of a recursive set under a total computable function is a recursive set.
Let e{\displaystyle e} be an index of the composition F∘ h{\displaystyle F\circ h},which is a total computable function.
That is, given such sets A and B,there is a total computable function f such that A{x: f(x)∈ B.
If the fundamental sequences are computable(e.g., as in the Wainer hierarchy),then every fα is a total computable function.
To complete the proof, let formula_6 be any total computable function, and construct formula_13 as above.
Is it possible to change the definition of a Turing machine so thata particular class of total Turing machines, computing all the total computable functions, can be found?
To complete the proof,let F{\displaystyle F} be any total computable function, and construct h{\displaystyle h} as above.
Topologically the class of total computable functions has been studied only in an extensional way as a subspace of a baire space and as an induced topology of an scott topology for the partial functions not necessarily computable. .
The image of a computable set under a total computable bijection is computable. .
A set A is many-one reducible to B if there is a total computable function f such that an element n is in A if and only if f(n) is in B. Such a function can be used to generate a Turing reduction by computing f(n), querying the oracle, and then interpreting the result.
The image of a computable set under a nondecreasing total computable function is computable. .
A many-one reduction from"A" to"B" is a total computable function"f": Σ*→ Γ* that has the property thateach word"w" is in"A" if and only if"f"("w") is in"B" that is, formula_1.
A set is recursive if andonly if it is either the range of a nondecreasing total computable function or the empty set.
A many-one reduction from A to B is a total computable function f: Σ*→ Γ* that has the property that each word w is in A if and only if f(w) is in B that is, A f- 1( B){\displaystyle A=f^{-1}B.
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest andearliest-discovered examples of a total computable function that is not primitive recursive.
Goodstein's theorem can be used to construct a total computable function that Peano arithmetic cannot prove to be total. .
Two questions can be asked about the relationship between partial Turing machines and total Turing machines: Can every partial function computable by a partial Turing machine be extended(that is, have its domain enlarged)to become a total computable function?
However the set of primitive recursive functions does not include every possible total computable function- this can be seen with a variant of Cantor's diagonal argument.
For any total computable function g for which g( x)≥ x{\displaystyle g(x)\geq x} for every x, there is a total computable function t such that with respect to Φ, the complexity classes with boundary functions t and g∘ t{\displaystyle g\circ t} are identical.
Formal definition==A subset of the natural numbers is called recursive if there exists a total computable function such that==Examples==*Every finite or cofinite subset of the natural numbers is computable. .
A is many-one reducible(or m-reducible)to B if there is a total computable function f such that each n is in A if and only if f(n) is in B. Truth-table reducibility A is truth-table reducible to B if A is Turing reducible to B via an oracle Turing machine that computes a total function regardless of the oracle it is given.
While Hilbert's tenth problem is not a formal mathematical statement as such, the nearly universal acceptance of the(philosophical)identification of a decision algorithm with a total computable predicate allows us to use the MRDP theorem to conclude that the tenth problem is unsolvable.
The strong reducibilities include:One-one reducibility A is one-one reducible(or 1-reducible) to B if there is a total computable injective function f such that each n is in A if and only if f(n) is in B. Many-one reducibility This is essentially one-one reducibility without the constraint that f be injective.