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 ...
متن کاملGetting around the Halting Problem
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.
متن کاملObservations on the Halting Problem
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...
متن کاملA Parameterized Halting Problem
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...
متن کاملAbelian p-groups and the Halting problem
We investigate which effectively presented abelian p-groups are isomorphic relative to the halting problem. The standard approach to this and similar questions uses the notion of ∆2-categoricity (to be defined). We partially reduce the description of ∆ 0 2-categorical p-groups of Ulm type 1 to the analogous problem for equivalence structures. Using this reduction, we solve to a problem left ope...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1974
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(74)80003-6