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Results tagged with computability
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user 42371
Questions related to computability theory, a.k.a. recursion theory
1
vote
The language of machines that accepts all palindromes is not Turing recognizable
Let $M_p$ be a TM that decides palindromes with runtime on $x$ at least $|x|$. Given $\langle M \rangle$ construct $\langle M' \rangle$ where $M'$ on $x$ behaves as follows:
Run $M$ on $\langle M \r …
- 1,503
3
votes
Is the set of TMs that does not reach most cells to the right computable?
Given a Turing Machine $M$ you can effectively construct $M'$ that does the following:
Given $x$, $M'$ overwrites $x$ with $\langle M\rangle$ up to length $|x|$ or end of $\langle M\rangle$, whichev …
- 1,503
5
votes
Accepted
Blank tape halting problem vs. Emptiness problem ($H_0$ vs. $E_{TM}$)
Yes, they are different. $L(M)$ is the set of all inputs accepted by a Turing machine, so $E_{TM}$ asks if a Turing machine doesn't accept any inputs. $H_0$ asks whether a particular input (the empty …
- 1,503
4
votes
Accepted
Prove that there is no computable enumeration of all decidable languages
WLOG assume we are talking about languages over a binary alphabet $\{0,1\}$. Let $M'$ be an enumerating Turing Machine for $L$, i.e., every element of $L$ is eventually output by $M'$. Let $\langle M_ …
- 1,503
2
votes
Accepted
Showing undecidability
I am interpreting the word "whenever" in the definition of $T$ to mean that $T$ consists of all pairs $\langle M, w \rangle$ such that either $M$ accepts $w$ and $w^R$ or $M$ rejects $w$ and $w^R$. Pl …
- 1,503