# Questions tagged [turing-machines]

The Turing machine is a fundamental model of computation, especially in theoretical work.

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### Any reason why Turing Machine would prevail on recursion theory? [migrated]

Nowadays, most introduction books, videos, and comments about theoretical computer science talk about Turing machines but don't discuss recursion theory anymore. These approaches are known to be ...
115 views

### How come Wikipedia says that Random Turing Machines can provide uncomputable output?

Wikipedia article mentioned : Hypercomputation The third paragraph starts off with: Technically, the output of a random Turing machine is uncomputable; however, most hypercomputing literature focuses ...
108 views

### What kind of computational model is the brain? [duplicate]

I was wondering what kind of computational model is the human brain (as it seems superior to a Turing machine). Another thing that should be a separate question, What would be a perfect computer model ...
96 views

### Can you diagnolize without mentioning simulation?

Are there any known diagonalization proofs, of a language not being in some complexity class, which do not explicitly mention simulation? The standard diagnolization argument goes: here is a list of ...
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### Given a program specification, S, what can be said about the size and efficiency of programs that exactly satsify S, with respect to the size of S?

Suppose we are given a program specification, $S$, and we want to reason about programs $P$ that satisfy $S$. One might like to think that if the specification is 'simple', the the program should be '...
681 views

### Is there any way to differentiate between “sort of” Turing-Complete and “really” Turing-Complete?

Some things, like the computer language C, turing machines, lambda calculus, etc. seem to be "naturally" Turing-Complete. That is, they're just Turing-Complete from the bottom up. On the other hand, ...
3k views

### A total language that only a Turing complete language can interpret

Any language which is not Turing complete can not write an interpreter for it self. I have no clue where I read that but I have seen it used a number of times. It seems like this gives rise to a kind ...
8k views

### How is proving a context free language to be ambiguous undecidable?

I've read somewhere that a Turing machine cannot compute this and it's therefore undecidable but why? Why is it computationally impossible for a machine to generate the parse tree's and make a ...
36 views

### Show that membership in L is undecidable [closed]

Let L ⸦ {0, 1}* be the language {(M, x) | Turing Machine M on input x enters every state of M at least once}. How can I show that membership in L is undecidable?
137 views

### Is $L \subset 1NL$ when $L \neq NL$?

A log-space Turing machine has a read-only input tape, a write-only output tape and uses at most $O(\log n)$ space in its read-write work tapes. The classes $L$ and $NL$ contain those languages which ...
116 views

### $DTIME_1(o(n^2))\setminus$ REGULAR

Maybe this is well-known, but I couldn't find any example of a non-regular lanugage that is decidable on a single-tape Turing machine in subquadratic time. Help! Related paper: On the structure of ...
238 views

### The power of randomized logspace with two-way access to the random tape

Let $\mathsf{ZPL}$/$\mathsf{RL}$/$\mathsf{BPL}$ denote the classes of the languages which are accepted (with zero/one-side/two-side error) by a logspace Turing machine with one-way access to the ...
211 views

### Prime factorisation of decidable problems

Disclaimer: I am not a theoretical computer scientist. The set of decidable problems $\mathbb{D}$ is countable so $\lvert \mathbb{D} \rvert = \lvert \mathbb{N} \rvert$ and this led me to the ...
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### Evidence integer multiplication is in linear time?

After millenia of quest we have identified two $n$ bit integers can be multiplied in $O(n\log n)$ time. Please refer details in https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-...
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### Did Alan Turing's student Robin Gandy assert that Charles Babbage had no notion of a universal computing machine?

Robin Gandy was a student of Alan Turing. Gandy did an analysis of Babbage's Analytical Engine (see 'Gandy - The Confluence of Ideas in 1936' quoted in 'Herken, Rolf - The Universal Turing Machine—...
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### Does Depth-First-Search admit a quasilinear time algorithm in mutitape Turing Machine model?

Depth-First-Search (DFS) has a quasilinear (i.e.,$\widetilde{O}(m+n)$) time algorithm in random access model (RAM). I am curious about whether DFS still admits a $\widetilde{O}(m+n)$ time algorithm in ...
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### Is Magic: the Gathering Turing complete?

A very specific question, I'm aware, and I doubt it will be answered by anyone that isn't already familiar with the rules of Magic. Cross-posted to Draw3Cards. Here are the comprehensive rules for the ...
2k views

### Oblivious Turing Machine emulation lower bound

Is there a proof that the emulation of a Turing machine on an oblivious Turing machine can't be done in less than $\mathcal{O}\left(m\log m\right)$ where $m$ is the number of steps the Turing machine ...
262 views

### Turing Machines as Coalgebras

I'm looking to write a survey on the method of representing the dynamics of state-based computation within the framework of coalgebras. So far I've managed to find papers on coalgebra representations ...
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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 ...
239 views

### Uniform mortality problem for Turing Machines

Consider the following generalisation of the mortality problem for Turing Machines. Given a Turing Machine $M$. Is there a bound $k_M$ such that starting from any configuration $c$ machine $M$ ...
510 views

### Langton's ant questions

I'm a mathematician currently working on the Langton's ant conjecture, just for fun. I have some result but I don't know if they are meaningless. So that is why I'm asking. 1) Is there a mathematical ...
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### Is there any research on Turing machines with transition relation homomorphic to given algebraic structure?

A Turing machine is defined as a structure $TM(L,Q,T)$, where $L,Q$ are sets of symbols and internal states of TM respectively, and T is a transition relation: $T: L \times Q \to L \times Q$ for ...
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### Functions that are Not Efficiently Computable but Learnable

We know that (see, e.g., Theorems 1 and 3 of ), roughly speaking, under suitable conditions, functions that can be efficiently computed by Turing machine in polynomial time ("efficiently computable"...
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### Why does the Placid Platypus function grow faster than any computable function?

I came across the Placid Platypus function $PP(n)$ today, defined as the minimal number of states needed for a turing machine that prints a string of $n$ ones and halts. This function is claimed to (...
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### P and NP classes explanation through lambda-calculus

In the introduction and explanation P and NP complexity classes often given through Turing machine. One of the model of computation is the lambda-calculus. I understand, that all of models of ...
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### Where does the modern canonical version of the Turing machine come from?

Turing's original 1936 description of his a-machine differs in several respects from the Turing machine I studied at university, leading me to questions: The Turing machine I learned about was ...