Questions tagged [universal-turing-machines]

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Asymptotic time required to simulate a Turing machine M for k steps

Problem: Given an encoding of a Turing machine M and a natural number k as input, find the output of M (given a blank tape) after k steps. Wikipedia's page on EXPTIME-complete says it takes O(k) time ...
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2answers
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For a specific unbounded Turing machine, is its Halting problem undecidable?

The question is on the title. To make it clearer, I state some facts. We all know that the Halting problem with input is undecidable. It leads to, given a specific input (e.g. empty string), the ...
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194 views

What is the VC dimension of Turing machines with specified maximum size?

Note by "maximum size" in the question I'm referring to the size of the Turing machine's state machine. I chose Turing machines in the question to make the question concrete, but I'm also more ...
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About reduction relation between $HP$ and $\mathcal{E}\mbox{*}$ [closed]

I'm studying Theory Of Computation and have some questions in the beginning: About reduction relation between $HP$ and $\mathcal{E}\mbox{*}$ $HP =$ {$<M,w>$ $|$ $M$ is a $TM$ and it halts on ...
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Can Pattern Recognition algorithms be considered Oracle Machines (in the Turing sense)?

I was reading Paul Churchland's "Engine of Reason, Seat of the Soul", where argues that humans (and potentially artificial neural networks as well) are capable of non-Turing computation because they ...
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Where can I find a Turing machine evaluating arithmetic expressions? [closed]

Is there a Turing machine that can evaluate arithmetic operations with brackets containing +, -, and ...
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1answer
649 views

Multi Head universal Turing machine

It is common knowledge that a universal Turing machine can simulate any Turing machine with logarithmic overhead. Is it possible to make this overhead constant by constructing an analogous "Universal" ...
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3answers
400 views

Fastest Turing Machine

Recently I have been reading about Kolmogorov Complexity. As such I started thinking about the "fastest turing machine". In particular I am not interested in finding such a machine, I am only ...
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1answer
310 views

Is my language Turing-complete?

Consider a language like Brainfuck but without the brackets. At the end of each line (i.e. when "\n" occurs), if the current cell is not 0, then the line is re-executed. An example of an infinite ...
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How much smaller can universal Turing machines get if they only need to be universal for a subclass?

Say that a Turing machine $U$ is universal for a class $\mathcal{C}$ of languages if for any language $L \in \mathcal{C}$, there is a word $w_L$ with: $$(\forall w)\quad w \in L \Leftrightarrow U(w_L, ...
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1answer
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Turing degree of Solomonoff semi-measure

We define the Solomonoff semi-measure $m$ on finite strings $x$ by $$m(x) = \sum_{p: U(p) = x} 2^{-l(p)},$$ where $U$ is a universal prefix Turing machine, $U(p) = x$ means $U$ outputs $x$ on input $...
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Can we not output the Kolmogorov complexity?

Let us fix a prefix-free encoding of Turing-machines and a universal Turing-machine $U$ that on input $(T,x)$ (encoded as the prefix-free code of $T$ followed by $x$) outputs whatever $T$ outputs on ...
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1answer
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Was bombe machine turing complete?

In the recent movie called The Imitation Game, there is a affirmation that Turing was building his theoretical machine. That machine is the Bombe Machine. Is this machine really equivalent to a Turing ...
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337 views

Is Kolmogorov complexity a surjective function?

Let us fix an encoding of Turing-machines and a universal Turing-machine, U, that on input (T,x) outputs whatever T outputs on input x (possibly both running forever). Define the Kolmogorov complexity ...
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What are different definitions of Universal Turing-machine?

I am not sure what is the appropriate way for this, but I would like to collect different possible definitions/variants of Universal Turing-machines. Here are the ones I know, post below if you know ...