Examples of using Partial recursive in English and their translations into Portuguese
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That is, S is the domain(co-range) of a partial recursive function.
Set" instead of"partial recursive function" and"recursively enumerable""r.e.
Then the function formula_4 is also a partial recursive function.
The broader class of partial recursive functions is defined by introducing an unbounded search operator.
Suppose{ e}{\displaystyle\{e\}} is the e{\displaystyle e}-th partial recursive function.
A total recursive function is a partial recursive function that is defined for every input.
Rice's theorem and index sets==Rice's theorem can be succinctly stated in terms of index sets::Let formula_48 be a class of partial recursive functions with index set formula_49.
And, in the context of partial recursive functions Kleene later admits a third outcome:"μ undecided.
Rice's theorem can be succinctly stated in terms of index sets: Let C{\displaystyle{\mathcal{C}}}be a class of partial recursive functions with index set C{\displaystyle C.
And suppose that that partial recursive function converges(to something, not necessarily zero) whenever formula_4 is defined and"y" is formula_4 or smaller.
The preimage of a recursively enumerable set under a partial recursive function is a recursively enumerable set.
Iii In the context of the partial recursive functions:Suppose that the relation"R" holds if and only if a partial recursive function converges to zero.
These researchers also use terminology such as partial computable function and computably enumerable(c.e.)set instead of partial recursive function and recursively enumerable(r.e.) set.
An equivalent definition states that a partial recursive function is one that can be computed by a Turing machine.
The instructions are drawn from the two classes to form"instruction-sets",such that an instruction set must allow the model to be Turing equivalent it must be able to compute any partial recursive function.
Relationship to recursive functions==The broader class of partial recursive functions is defined by introducing an unbounded search operator.
In the equivalence of models of computability, a parallel is drawn between Turing machines that do not terminate for certain inputs andan undefined result for that input in the corresponding partial recursive function.
Offers a 3-valued logic for the cases when algorithms involving partial recursive functions may not return values, but rather end up with circumstances"u" undecided.
Now if Q(x)is a partial recursive predicate, there is a decision procedure for Q(x) on its range of definition, so the law of the excluded middle or excluded"third"(saying that, Q(x) is either t or f) applies intuitionistically on the range of definition.
The statement of the theorems refers to an admissible numbering φ{\displaystyle\varphi} of the partial recursive functions, such that the function corresponding to index e{\displaystyle e} is φ e{\displaystyle\varphi_{e.
Equivalence with other models of computability==In the equivalence of models of computability, a parallel is drawn between Turing machines that do not terminate for certain inputs andan undefined result for that input in the corresponding partial recursive function.
It is proved(Burgin, 2005) that limiting partial recursive functions, trial and error predicates, general Turing machines, and simple inductive Turing machines are equivalent models of computation.
Posteriorly, such versions were extended in order to also include the partial algorithmic functions, giving rise, in this way,to the version of the partial recursive functions and to the version of the partially turing-computable functions.
A set S of natural numbers is called recursively enumerable if there is a partial recursive function whose domain is exactly S, meaning that the function is defined if and only if its input is a member of S. The following are all equivalent properties of a set S of natural numbers: Semidecidability: The set S is recursively enumerable.
Example of a 3-valued logic applied to vague(undetermined) cases: Kleene 1952(§64, pp. 332-340)offers a 3-valued logic for the cases when algorithms involving partial recursive functions may not return values, but rather end up with circumstances"u" undecided.
Given a partial function"f" from the natural numbers into the natural numbers,"f" is a partial recursive function if and only if the graph of"f", that is, the set of all pairs formula_11 such that"f(x)" is defined, is recursively enumerable.
Each enumeration operator Φ determines a function from sets of naturals to sets of naturals given by: formula_76A recursive operator is an enumeration operator that,when given the graph of a partial recursive function, always returns the graph of a partial recursive function.
Simple inductive Turing machines andgeneral Turing machines are related to limiting partial recursive functions and trial and error predicates as Turing machines are related to partial recursive functions and lambda-calculus.
Each enumeration operator Φ determines a function from sets of naturals to sets of naturals given by Φ( X){ n∣∃ A⊆ X}.{\displaystyle\Phi( X)=\{ n\ mid\ exists A\ subseteq X\}.} A recursive operator is an enumeration operator that,when given the graph of a partial recursive function, always returns the graph of a partial recursive function.
Formal definition==A set"S" of natural numbers is called recursively enumerable if there is a partial recursive function whose domain is exactly"S", meaning that the function is defined if and only if its input is a member of"S.