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Questions tagged [turing-machines]

This tag is suited for questions involving Turing machines. Not to be confused with finite state machines and finite automata.

954 questions
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Are there any Turing-undecidable problems whose undecidability is independent of the Halting problem?

To be more specific, does there exist a decision problem $P$ such that given an oracle machine solving $P$, the Halting problem remains undecidable, and given an oracle machine solving the Halting problem, $P$ remains undecidable?
David Zhang
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Exactly when and why can a Turing-machine not solve the halting problem?

I perfectly understand and accept the proof that a Turing-machine cannot solve the halting problem. Indeed, this is not one of those questions that challenges the proof or result. However, I feel that there is still something left to be explained…
Bram28
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Length of the longest non-infinite path given by a pattern of length n.

Before I get into it, my question is what's the next step in finding the longest path for a pattern length $n$? Imagine if you will, an integer grid. You start a bot off at $(0,0)$ with a pattern, [left, right, no turn, no turn, left, right] which…
Jacob Claassen
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Lower bounds for bb(7) and bb(8) wanted

The busy beaver function $bb(n)$ is not known for $n \geq 5$. Does Anyone know suitable lower bounds for $bb(7)$ and $bb(8)$? Remark: $bb(6)$ as a trivial lower bound does not count as a suitable bound.
Peter
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5
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How was the busy beaver candidate for 6 states calculated?

The current busy beaver candidate on 6 states, with the original binary alphabet configuration, produces about 10^18267 1's, according to the wiki page on Busy Beaver. I could not find any working links to research that further. My question is, what…
jack
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1 answer

Are Turing machines that move before assigning Turing complete?

A state in a Turing machine is an assignment and a move direction both depending on the current input. But if we define Turing machines to be a move first and then an assignment both depending on the current input, would this also be Turing…
zooby
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Why is there no computable function that grows faster than the sequence of Busy Beaver numbers?

I understand that if f Grows faster than BB Is computable Can be proven to have the first property we can use it as an oracle to solve the halting problem. But let's say f is computable, grows faster than BB but cannot be proven to grow faster…
azani
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4
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Could we design a Turing machine that output every bit of $\pi$ one after another correctly with limited tape length?

Could we design a Turing machine that output every bit of $\pi$ one after another correctly? I think the answer is yes because we have computer programs that calculate the value of $\pi$ day after day forever, and thus it's viable. However, could we…
Frank Xu
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What's the meaning of Oblivious Turing Machine

I really don't understand the the difference between OTM and Standard TM. Could any explain it for me? Thanks
Boyuan Yan
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Read head of a STANDARD Turing machine

In classes it has been explained to us that for a Turing machine to be standard it needs an infinite tape in both directions, a reading head and transitions, where the reading head can move to the left or to the right. I am currently doing an…
Sebastian
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A version of a Turing maching that can cut out and/or remove tape squares

I would like to know if in the literature there have been considered versions of Turing machines that, instead of changing the content of one tape square at a time are allowed to perform more general moves, particularly adding new squares to the…
Ilya Kapovich
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Is a Turing Machine with access to an entropy source "more powerful" than an ordinary TM?

I'm wondering whether a Turing Machine with access to a random number generator is equivalent in power to an ordinary Turing Machine. The RNG is implemented here as a privileged instruction that reads a $0$ or $1$ from an otherwise inaccessible…
Greg Nisbet
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3
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Turing machine which deletes half of input

I am looking to define a Turing machine which takes in a tape of $2n$ $1$'s surrounded by infinite $0$'s e.g., $...0000111111110000...$ and has an end configuration of half of those $1$'s e.g., $...0001111000...$. Here are my thoughts: I am thinking…
Raton
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How can a turing machine solve the element distinctness problem?

I am reading an example in Sipser's famous book on the theory of computation. In this example, Sipser creates a turing machine M to solve the element distinctness problem. M is given a list of strings over $\Sigma = \{0, 1\}$ separated by #s. M must…
John Hoffman
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Using Extended Rice's Theorem to Prove Decidability

I have a Turing Machine M. Let L be the set of all strings representing the encoding of M that has input alphabet {1,2}, where M accepts infinitely many strings that start with 1 and finitely many strings that start with 2. I'm trying to determine…
Amal Kahalee
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