# Questions tagged [turing-machines]

Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

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### Prove $L = \{M \mid L(M)\text{ is infinite}\}$ is not Turing-recognizable

I'm supposed to prove this through mapping reducibility. I think I'm supposed to show that $A_{\mathrm{TM}} \le_\mathrm{m}\overline{L}$, which means that $\overline{A_{\mathrm{TM}}}\le_\mathrm{m} L$ ...
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### Can I program a universal Turing machine to accept arbitrary input encodings?

I've been reading about building Turing machines for specific purposes, and some sources talk about input encodings and some talk about programming specific machines, but I've been unable to find ...
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### Prove that it is undecidable whether a given LBA accepts a regular set

I know for an LBA the emptiness problem is undecidable. However I am not clear on how to reduce the halting problem of Turing machines to this as LBAs are strictly computationally less powerful than ...
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### Does Multitape reduction to a one tape machine preserve space complexity?

Suppose a Turing machine $M$ has a read-only input-tape and $k$ read-write work-tapes whose non-blank cells are each bounded by $f(|x|)$ where $|x|$ is the length of the input. Is there some constant ...
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### Cardinality of the set of algorithms

Someone in a discussion brought up that (he reckons) there can be at least continuum number of strategies to approach a specific problem. The specific problem was trading strategies (not algorithms ...
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### QTM & Halting problem [duplicate]

"Can QTM (Quantum Turing machine) solve halting problem" Why not have an immediate answer "No QTM Can't do this", we know that Turing proved it impossible when DTM , i meant , " Why we cant use the ...
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### Is every von neumann machine turing complete? [duplicate]

I understand that TM is a 'Model of Computation' which tells us about the computational power of a machine while Von Neumann Architecture is a 'System Architecture' that tells us about how the machine ...
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### Determine in which class $L=\big\{\langle M_1,M_2,w\rangle\mid M_1,M_2\text{ are TM and }L(M_1)\cap L(M_2)=\{w\}\big\}$

my solution is that $L\in co-RE$ by showing that $\overline{L}\in RE$ TM $M$ on input:$\langle M_1,M_2,w\rangle$ Build TM $M_1,M_2$ Simulate $M_1$ on $x\in\Sigma^*$, before that check if $x\neq w$ ...
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### Prove {0^n OR 1^2n OR 2^3n | n >= 0} is not context free

How to prove using pumping lemma {0^n OR 1^2n OR 2^3n | n >= 0} is not context free This isnt the same language as {0^n1^2n2^3n | n >= 0} as this language the numbers need to be in order.
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### SAT Solving + Turing Machines

I have a couple of questions based on how SAT solvers work. I understand that SAT solvers may employ any/all of the following techniques: Randomness Heuristics Backtracking SAT is just one example ...
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### If $L=\big\{\langle M_1,M_2\rangle\mid M_1, M_2\text{ are TM and } L(M_1)\cup L(M_1)=\Sigma^* \big\}$ is in $RE$ or $coRE$ or not in $RE\cup coRE$?

I tried to solve it as the following: $$\overline{L}=\big\{\langle M_1,M_2\rangle\mid M_1, M_2\text{ are TM and } L(M_1)\cup L(M_1)\neq\Sigma^* \big\}$$ I'll show that $\overline{L}\not\in RE$ by ...
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### Turing machine that accepts L = {a^nb^2n : n ≥ 0}

write a Turing machine that accepts L = {a^nb^2n:n ≥ 0} where there are double the amount of b's in comparisons to the amount of a's. So aabbbb would be accepted but aabbaabb would not. I am unsure of ...