Construction theory, self-replication, and the halting problem
نویسندگان
چکیده
منابع مشابه
On self-replication and the halting problem
This short Letter elucidates a fundamental relationship between self-replication of living systems and the halting problem in computation theory.
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We present a formalization of the halting problem in Agda, a language based on Martin-Löf’s intuitionistic type theory. The key features are: – We give a constructive proof of the halting problem. The “constructive halting problem” is a natural reformulation of the classic variant. – A new abstract model of computation is introduced, in type theory. – The undecidability of the halting problem i...
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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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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: Complexity
سال: 2008
ISSN: 1076-2787,1099-0526
DOI: 10.1002/cplx.20218