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 ...
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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 ...
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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 ...
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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 '...
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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, ...
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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 ...
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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 ...
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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?
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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 ...
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$DTIME_1(o(n^2))\setminus$ 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 ...
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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 ...
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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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Can $\mathsf{P}^{\#\mathsf{P}}$ be described in terms of a non-deterministic (alternating) Turing machine?

Can the $\mathsf{P}^{\#\mathsf{P}}$ (= $\mathsf{P}^{\mathsf{PP}}$) class be described in terms of a non-deterministic Turing machine (in particular, an alternating Turing machine)? And would a $\...
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Definition of a prefix-free Turing machine

A prefix-free function is one whose domain is prefix-free. Similarly, a prefix-free (Turing) machine is one whose domain is prefix-free. It is usual to consider such a machine as being self-...
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Is the decidability of a language decidable? [closed]

Is there a Turing machine that takes a language as input and decides/semi-decides if it is a decidable language? Comments + answer say trivially the answer is yes; however, I'm wondering here would ...
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Why NL is not L

I'm a beginner in learning complexity and get confused at NL. NL is the class of languages that are decidable in logarithmic space on a nondeterministic Turing machine. In other words, NL = NSPACE($\...
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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 ...
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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 ...
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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 ...
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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 $M$ ...
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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 [1]), 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 ...
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Do Turing complete languages automatically have efficient algorithms [closed]

Every Turing complete programming language can describe an algorithm that sorts sequences. Is it also true that every Turing complete language can describe an algorithm that sorts sequences in $\...
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Minimal information needed for determine some function

From calculus, we know that if someone has a continuous function $f$, it is enough to know $f$'s values on the rationals in order to know $f$ on the entire line. In some sense, a "countable amount of ...
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Are all turing machines paths predictable?

I was recently studying partial solutions to the halting problem and came across the problem which I discuss below. In particular I was studying when it was computable to tell if a turing machine has ...
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Solving the Halting problem for most inputs [closed]

Is it possible to solve the following version of the Halting problem : given any Turing machine and some input tape, the program should answer if this pair halts or not except possibly for one Turing ...
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Question About Turing Machine Computability [closed]

If p is a Turing machine then L(p) = {x | p(x) = yes}. Let A = {p | p is a Turing machine and L(p) is a finite set}. Is A computable? Justify your answer. So I'm trying to figure out how to solve ...
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Libraries for programming automata and Turing machines

What are the most useful libraries around for coding related to automata and Turing machines? By useful I mean the number of functions and algorithms supported by it.
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Games on Turing machines that are AH-hard

I'm interested in proving that finding optimal play in a particular two-player game is harder than the arithmetic hierarchy. I suspect this to be true, because even carrying out a deterministic end-...
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What is the practical importance of making or using a Turing complete language? [closed]

I get what a Turing machine is and what language is a Turing-complete language but when someone introduces me to a new programming language (like Solidity) and says it is Turing complete, what am I ...
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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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How good can a halting detector be?

Is there a Turing Machine that can decide whether almost all other Turing Machines halt? Suppose we have some enumeration $\mathbb{N} \rightarrow \{M_i\}$ of Turing machines, and some notion of "...
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Was Babbage's Analytical Engine really turing-complete?

According to literature, Babbage's Analytical Engine is turing-complete because it supports conditional branching: it can perform different operations depending on the sign of the result last ...
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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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Enumerating decidable languages

[The assumption in this question is wrong. It is possible to enumerate exactly the decidable languages with semideciders.] Lets say we have a TM $M_E$ enumerator that writes out codes of TM's on a ...
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Turing machines over a structure

I have heard of models of computation where you have a Turing machine, but instead of symbols over a finite alphabet you have elements from some tau-structure, and write instructions are replaced with ...
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Real computers have only a finite number of states, so what is the relevance of Turing machines to real computers?

Real computers have limited memory and only a finite number of states. So they are essentially finite automata. Why do theoretical computer scientists use the Turing machines (and other equivalent ...
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What is the time complexity of base conversion on a multi-tape Turing machine?

Base conversion is the problem of converting an integer between representations in two fixed bases. Without loss of generality consider the case of relatively prime bases. I think it's easier to ...
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Compressing information about the halting problem for oracle Turing machines

The halting problem is well-known to be uncomputable. However, it is possible to exponentially "compress" information about the halting problem, so that decompressing it is computable. More precisely,...
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How fast can we sort a list if we know how it was written?

Let $G$ be a linear time (deterministic) turing machine that takes positive integers $n$ in unary to lists of length $n.$ For any fixed such $G$, define sparse-sort(G,n) as the problem of sorting the ...
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What's the differences between “A language is computable by a TM” and “A language can be decided by a TM”? [closed]

I am reading two books about the Turing Machine. "Computational Complexity" by Christos H. Papadimitriou. "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak. However, the ...