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Results tagged with computability-theory
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user 8381
computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
2
votes
2
answers
395
views
Absolutely algorithmically random infinite sequence
Let's call an infinite sequence of bits $f:N\rightarrow \{0,1\}$ absolutely random if any computably constructed subsequence is not computable, i.e. there aren't monotonic computable function $g:N \ri …
- 1,278
4
votes
1
answer
454
views
On fast-growing hierarchy
Is there exists a recursively enumerable set of computable total fast-growing functions $(\mathbb N \rightarrow \mathbb N)$ such, that this set has no upper boundary in the set of all such functions ( …
- 1,278
7
votes
1
answer
2k
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Ackermann function in the Primitive recursive arithmetic
Hello.
I study primitive recursive arithmetic and have the following questions.
1) Is it possible to express in the PRA that Ackermann function is total?
2) If yes, is such expression decidable in …
- 1,278
30
votes
11
answers
6k
views
Physics and Church–Turing Thesis
Is there constructed some set of physical laws from which we can logically obtain that any function that can be implemented in some device is Turing computable?
EDIT
I believe that if we restrict ou …
- 1,278
3
votes
0
answers
247
views
An alternative definition of computable ordinals
An ordinal $\alpha$ is said to be computable if there is a computable relation on a subset of integers that is well-ordered and its order type equals $\alpha$.
But let's consider well-founded trees on …
- 1,278