Examples of using Total function in English and their translations into Portuguese
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Kleene makes it as a total function instead cf.
Total functions defined by the six recursion operators.
Some algorithms in their default form may require total functions.
This is a total function since every Goodstein sequence terminates.
Types of numberings==A numbering is total if it is a total function.
It affects the total functioning of the liver by preventing the absorption of nutrients and removal of toxic substances from the blood.
In particular 1/0∞, and moreover 1/∞ 0, making reciprocal,1/x, a total function in this structure.
Footnotes===== Total function demonstration===What is"mandatory" if the function is to be a total function is a demonstration"by some other method" e.g.
Stated otherwise: The Trinity Absolute, as its name implies,is really absolute in total function.
A Turing machine implementing a strong reducibility will compute a total function regardless of which oracle it is presented with.
Following are some relevant points of interest about fast-growing hierarchies:Every fα is a total function.
In order to produce a computable real, a Turing machine must compute a total function, but the corresponding decision problem is in Turing degree 0′′.
This idea can be used to show that the machine is incorrect on some sequences if it computes a total function.
In a function problem a single output(of a total function) is expected for every input, but the output is more complex than that of a decision problem, that is, it isn't just"yes" or"no.
The set of natural numbers that are indices for Turing machines that compute total functions is formula_124.
A religious mind is concerned with the totality not with a particular function, but with the total functioning of human existence.
McCarthy Formalism What is mandatory if the function is to be a total function is a demonstration by some other method(e.g. induction) that for each and every combination of values of its parameters xi some natural number y will satisfy the μ-operator so that the algorithm that represents the calculation can terminate:"… we must always hesitate to assume that a system of equations really defines a general-recursive function. .
The set of natural numbers that are indices for Turing machines that compute total functions is Π 2 0{\displaystyle\Pi_{2}^{0.
But because Peano arithmetic does not prove that every Goodstein sequence terminates,Peano arithmetic does not prove that this Turing machine computes a total function.
Therefore it can't be total, butthe function by construction must be total(if total functions are recursively enumerable, then this function can be constructed), so we have a contradiction.
Each finite sequence can be identified with a partial function from formula_2 to itself, andeach infinite path can be identified with a total function.
Therefore, it cannot be total, butthe function by construction must be total(if total functions are recursively enumerable, then this function can be constructed), which is a contradiction.
Each finite sequence can be identified with a partial function from ω{\displaystyle\omega} to itself, andeach infinite path can be identified with a total function.
In computational complexity theory,a function problem is a computational problem where a single output(of a total function) is expected for every input, but the output is more complex than that of a decision problem.
Variations from 0 to± 10% arewithin normality deviations for the formula, with zero percent representing normal function and -100% representing total function loss.
Thus if this new model of computation consisted of asequence formula_1 of machines, there would be a recursively enumerable sequence formula_2 of Turing machines that compute total functions and so that every total computable function is computable by one of the machines"Ti.
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.
With this matter settled, he demonstrates with single"Proof III" that either types(a) or(b) together with the five primitive recursive operators yield the(total)recursive functions… with this proviso for a total function: That for all parameters x, a demonstration that must be provided to show that a y exists that satisfies(a) μy ψ(x, y) or(b) μy Rx, y.
Thus if this new model of computation consisted of a sequence M 1, M 2,…{\displaystyle M_{1}, M_{2},\ldots} of machines, there would be a recursively enumerable sequence T 1,… T 2,…{\displaystyle T_{1},\ldots T_{2},\ldots}of Turing machines that compute total functions and so that every total computable function is computable by one of the machines Ti.