Examples of using Halting problem in English and their translations into Greek
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Startling as the halting problem was, the really profound part of Incompleteness for Turing,
by representing the halting problem in this way.
including many different sets that encode variants of the halting problem, have two properties in common:
in the Turing degree of the halting problem.
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation,
that could solve the halting problem for a Turing machine amongst other things.
Decidability of Languages, Halting Problem, Reductions.
Jack Copeland(2004) attributes the term"halting problem" to Martin Davis.
Kleene showed that the existence of a complete effective theory of arithmetic with certain consistency properties would force the halting problem to be decidable, a contradiction.
Kleene showed that the existence of a complete effective system of arithmetic with certain consistency properties would force the halting problem to be decidable, a contradiction.
and thus the halting problem is the most complicated recursively enumerable set with respect to many-one reducibility
Since the negative answer to the halting problem shows that there are problems that cannot be solved by a Turing machine, the Church- Turing
a theorem of Friedburg shows that any set that computes the Halting problem can be obtained as the Turing jump of another set.
Post showed in 1954 that there are intermediate Turing degrees between those of the computable sets and the halting problem, but they failed to show that any of these degrees contains a recursively enumerable set.
has the property that either the halting problem or its complement is many-one reducible to E,
the Turing jump of A is a set of natural numbers encoding a solution to the halting problem for oracle Turing machines running with oracle A. The Turing jump of any set is always of higher Turing degree than the original set, and a theorem of Friedburg shows that any set that computes the Halting problem can be obtained as the Turing jump of another set.
Halting problem.
The halting problem is undecidable for Turing machines.
Is Turing's'halting problem'.
The halting problem is undecidable over Turing machines.