Short notes: The Halting Problem Does Not Matter
نویسندگان
چکیده
منابع مشابه
Approximations to the Halting Problem
The halting set Kr = (x I r converges}, for any G6del numbering ~ = {~0, ~1 ,-..}, is nonrecursive. It may be possible, however, to approximate Kr by recursive s e t s . We note several results indicating that the degrees of recursive approximability of halting sets in arbitrary GSdel numberings have wide variation, while restriction to "optimal GSdel numberings" only narrows the possibilities ...
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The Halting Theorem establishes that there is no machine H that can decide in all cases if a machine n halts on input m. The conjecture of this paper is that nevertheless there exist a machine H such that it can identify all the cases it is unable to decide. This become possible if the Recursion Theorem is reinterpreted as mutual necessitation rather than equivalence.
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When Alan Turing laid the foundation for computation in 1936, he wanted to show what computation can do, and what it cannot do. For the latter, he invented a problem that we now call the “Halting Problem”. In modern terms, it is as follows. In a general-purpose programming language, write a program that reads a text (character string) p representing a program in that same language, and reads an...
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The parameterized problem p-Halt takes as input a nondeterministic Turing machine M and a natural number n, the size of M being the parameter. It asks whether every accepting run of M on empty input tape takes more than n steps. This problem is in the class XPuni, the class “uniform XP,” if there is an algorithm deciding it, which for fixed machine M runs in time polynomial in n. It turns out t...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1984
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/27.4.376