Examples of using Halting problem in English and their translations into Greek
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Halting problem.
Represents the halting problem.
Halting problem- Wikipedia.
Is Turing's'halting problem'.
The halting problem is undecidable for Turing machines.
This problem is known as the Halting problem.
The Halting problem was the first such set to be constructed.
One such problem is known as the Halting Problem.
The halting problem is historically important because it was one of the first problems to be proved undecidable.
These numbers have the same Turing degree as the halting problem.
His argument is fundamental in the solution of the Halting problem and the proof of Gödel's first incompleteness theorem.
This means that this gives us an algorithm to decide the halting problem.
His argument is fundamental in the solution of the Halting problem and the proof of Gödel's first incompleteness theorem. Cantor wrote on the Goldbach conjecture in 1894.
There is a noncomputable problem, the Halting problem.
Turing proved this by establishing the unsolvability of the halting problem, a result with far-ranging implications in both recursion theory and computer science.
But, many of these index sets are even more complicated than the halting problem.
Startling as the halting problem was, the really profound part of Incompleteness for Turing, was not what it said about logic or computers, but what it said about us, and our minds.
Is undecidable, by representing the halting problem in this way.
In fact, a weaker form of the First Incompleteness Theorem is an easy consequence of the undecidability of the halting problem.
Jack Copeland(2004) attributes the introduction of the term halting problem to the work of Martin Davis in the 1950s.
Conway proved that the problem: Given g and n, does the sequence of iterates g k( n){\displaystyle g^{k}(n)} reach 1? is undecidable,by representing the halting problem in this way.
The natural examples of sets that are not computable,including many different sets that encode variants of the halting problem, have two properties in common: They are recursively enumerable, and Each can be translated into any other via a many-one reduction.
Even more difficult are the undecidable problems, such as the halting problem.
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine.
Rice's theorem generalizes the theorem that the halting problem is unsolvable.
Post's original motivation in the study of this lattice was to find a structural notion such that every set which satisfies this property is neither in the Turing degree of the recursive sets norin the Turing degree of the halting problem.
Post showed that these sets are strictly between the computable sets and the halting problem with respect to many-one reducibility.
It is an open question whether there can be actual deterministic physical processes that, in the long run, elude simulation by a Turing machine, and in particular whether any such hypothetical process could usefully be harnessed in the form of a calculating machine(a hypercomputer)that could solve the halting problem for a Turing machine amongst other things.
Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible inputs cannot exist.
This result dates from the works of Church, Gödel andTuring in the 1930s(see: Halting problem and Rice's theorem).