Turing Definition and 57 Threads

  1. F

    Insights P vs. NP conjecture and what is a Turing Machine (TM)?

    Continue reading ...
  2. PainterGuy

    Is Alan Turing given too much credit when it comes to computers?

    Hi, Is Alan Turing given too much credit when it comes to computers? He is presented as someone who played a pivotal role with the realization of a computer. What Turing did as an answer to Hilbert's problem was a great achievement from mathematical point of view. Alan Turing was mathematician...
  3. T

    Have a Turing Machine? Can it solve linear algebraic equations?

    I don't understand the Turing Machine. Amazingly this hypothetical device, designed in the 1930s can do everything the most powerful computers can do today, but it would just take much longer. Has anybody ever built one just to solve a simple linear algebraic equation? How long would the tape...
  4. F

    Python Explore Alan Turing's Computable Numbers & Generate Pi with Python

    I found this article about Alan Turing and his concept of Turing machines on the AMS website. Since we often get questions about countability and computability I thought it is worth sharing. https://blogs.ams.org/featurecolumn/2021/12/01/alan-turing-computable-numbers/ It also contains a Python...
  5. BillTre

    Turing Prize goes to Pixar Computer Graphics Pioneers

    Here is a NY Times article on this. They were recognized for their work on three-dimensional computer graphics and get $1,000,000. Besides Hollywood special effects, their techniques are used in video games, and virtual reality (more useful now in the age of social distancing).
  6. GlenLaRocca

    Turing Test: Respectful Criticism and Cultural Differences

    Summary: Turing I have great respect for nearly all of Turing's work but as for the Turing Test I have a lot of problems. My life has taken me through many layers of the socio-economic spectrum, and I have learned a few things about my fellow humans that Turing may not have had the...
  7. M

    MHB Is this a Gödel number of a Turing machine?

    Hey! :o We have the number \begin{align*}70&6737922567786324304462189150536772513339293263220644 \\ &=2^2\cdot 3\cdot 59^5\cdot 103\cdot 149^2\cdot 353\cdot 607\cdot 823^4\cdot 1409\cdot 1873^2\cdot 4201^3\end{align*} I want to check if this is a Gödel number of a Turing machine. From...
  8. M

    MHB Reducing States in Modified Turing Machines

    Hey! :o I am looking at the following: The Turing table of the following modified Turing machine is given: Change this into an ordinary "Turing machine" (i.e., one that either writes or moves the head). Give the appropriate Turing table. Give also the Turing table of an equivalent...
  9. W

    Comp Sci Problem on undecidable problems

    I should first note that I am not a compsci student, and have not learned the "formal" way of using "Languages" to solve such problems. All I have are the two definitions provided above. Thanks! 1b) This is the Halting problem: Undecidable 1c) I have a feeling that this is decidable, since if...
  10. L

    Design an Infinite NTM for Any Input String: Turing Machine Question

    Hey guys just wondering if I could get some help with this question. I am having trouble with it as I don't know what the input language is and therefore what inputs to handle. Heres the question: Design an NTM (normalised Turing machine) that never terminates, so that regardless of the input...
  11. G

    I Can Turing Machines Understand Infinity?

    I had a conversation with someone once upon a time (it was quite a while back actually), and we came to the question of whether or not Turing machines could ever understand infinity. We agreed that we as humans are intimate with the extant and divisible infinities mainly through our...
  12. binbagsss

    Mathematical Biology- Neumann BCs, Turing Analysis

    This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reaction-diffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,...,x_n,t)## is a scalar I believe? so that ##...
  13. 2

    Is this a Turing-complete machine?

    Say a Turing machine is simulated by the following rules: A number of states can be defined. Each state is defined by : specifying what the head writes in the current cell in case of each symbol of the alphabet specifying where the head moves (left or right) in case of each symbol of the...
  14. ShayanJ

    A brain-like implementation of a Turing machine

    At first I should say that this thread involves many scientific fields and I don't think there is any correct section of PF to put it under so I just went with the engineering. One of the greatest mysteries(maybe the greatest) that science is trying to solve today, is the emergence of...
  15. cobalt124

    I Enumerate all 1-state Turing Machines

    Hi, using the definition of a TM from https://en.wikipedia.org/wiki/Busy_beaver a 1-state TM would have: one "operational" state a, plus the Halt State h a tape alphabet of 0,1 a tape initially all zeros Given this the possible 5-tuples a 1-state TM transition table could have are: (current...
  16. nomadreid

    I Would Infinite Time Resolve the Halting Problem?

    The short version: If you had an infinite amount of time, would the standard proof for the insolubility of the halting problem still work? The longer version: A simple proof that there are non-computable functions can be easily seen by the fact that there are only countable number of Turing...
  17. G

    Turing Machines: Classifying for Decidable Problems

    It's been a while since I've done this, but the question spurred on. Is there any sort of named class that a machine that can decide on all Turing decidable problems would belong to? Edit: Actually, I guess it would be Turing if you could program it to decide on a particular problem.
  18. M

    MHB Designing a Non-deterministic 2-Tape Turing Machine for a Specific Language

    Hey! :o I want to find a non-deterministic 2-tape Turing machine, that accepts the language L over $\Sigma=\{0,1\}$ in $n$ steps, with input of length $n$, $L=\{x1y \mid |y|=2|x|>0\}$. Should the Turing machine do the following? (Wondering) Each time that the machine reads 1 it should check...
  19. M

    MHB Non-deterministic 2-tape Turing Machine

    Hey! :o I want to find a non-deterministic $2$-tape Turing Machine, that accepts the language $L$ over $\Sigma=\{0,1,\#\}$ in linear time, $$L=\{x\#y \mid x,y \in \{0,1\}^\star, x \text{ is contained in } y\}$$ Does the Turing Machine look as follows? The tape $1$ contains the input $w$ and...
  20. B

    [Theoretical computer science] Regular Turing Machine undecidable proof

    Hello the proof of the Spiser's book (introduction to theory of computation): PROOF We let R be a TM that decides REGULARTM and construct TM S to decide ATM. Then S works in the following manner. S = "On input (M, w), where M is a TM and w is a string: 1...
  21. M

    MHB Solving Recursive Sets with Turing Machines

    Hey! :o I have to show that a set is recursive if and only if the set and its complement is recursively enumerable. I have done the following: $\Rightarrow$ Let $A$ the recursive set, so there is a Turing machine $M$ that decides the set $A$. We construct a TM $M'$ that semi-decides the set...
  22. M

    How the original Turing machine broke the enigma

    I just saw The Imitation Game and was wondering how the original Turing machine broke the enigma. Could someone explain it to me?
  23. B

    Symbol in Alan Turing's On Computable Numbers

    In Alan Turing's On Computable Numbers, he explains in his second paragraph the general notion of computable numbers. In doing so, he writes "In [symbol][symbol] 9, 10 I give some arguments...". I will include a screenshot of these symbols in this post. Do any of you know what these symbols...
  24. J

    Numerically solving system of four PDEs

    Hi Forum, I'm trying to use Mathematica to graphically explore a system of four PDEs, as defined in Yang et al. (2002). Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes. Physical Review Letters 88(20). The equations are: \frac{\partial...
  25. mishima

    Help explain this Turing machine notation

    Below is an image from a website article discussing a Turing machine. It is supposed to represent a Turing machine, but I don't really follow the notation. I assume this is part of Wolfram's book, "New Kind of Science", which I do not have a copy of. I have only ever seen a Turing machine...
  26. J

    Help plotting interacting Turing modes

    Hello, everybody. I'm trying to replicate plots from Yang et al. 2002. Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes. Phys. Rev. 88(20) using Mathematica, to explore specifically under what parameter values the pattern of...
  27. D

    Can Turing Machines Be Represented by Polynomial-Sized Circuits?

    How do you show that every polynomial-time turing machine has a family of equivalent polynomial-sized circuits?
  28. S

    Can a Turing Machine Execute Multiple Programs?

    Hi: I read many articles about turing machine,but i still confused:confused: is a turing machine can only execute one program(hardwired) ? or it can execute many programs(like a conventional computer)? i asking about turing machine as shown in figure blew(not asking about universal TM...
  29. P

    Why Turing Machines are important

    Can someone explain to me, one with extremely limited knowledge of the concept of Turing Machines, what these hypothetical machines help us understand or accomplish in computer science?
  30. Jim Kata

    Turing Completeness Lambda Calculus

    I have been kind of trying to teach myself some ideas from CS. What does Turing completeness mean exactly? For example, Lambda Calculus is Turing complete. What does that mean and how do you prove that?
  31. nomadreid

    Probabilitstic versus non-deterministic Turing machines

    Although this question is more theoretical than most of the threads in this rubric, it still seems to me to fit the description "Computer Science". If I am wrong, perhaps someone would tell me where the question belongs. The question is as follows: After reading the descriptions of...
  32. M

    Turing machine problem to getting startet

    Good everning! I am currently working on problems related to turing machines. Lets say we have a turing machine T . Vi can see the Turing machine driving in state 1, state 2 and so forth. If we do this we can set it up as a table. see under. in my head it will look like this (R is a...
  33. A

    Philosophical: Is the universe a type of Turing machine?

    Here is a fun philosophical question I wonder about sometimes, given that my background is in computer science and not physics. In the field of computer science, a Turing Machine is considered to be able to carry out any computation. So, philosophically, could the universe be thought of as a...
  34. A

    Set cardinality, Turing encoding, and inductive proofs

    I'm going to construct an ordered set, and I'd like to ask some questions about it; and in particular consider coding problems about this set and sets in general (Turing tape encoding). Start with: A={ } And, allow a mutable temporary set, initialized with: T={ } and an iterator: set n=0 For...
  35. P

    MHB Remembering Alan Turing: A Pioneering Computer Scientist

    http://chronicle.com/blogs/linguafranca/2012/06/28/remembering-alan-turing/?cid=at&utm_source=at&utm_medium=en.
  36. zoobyshoe

    Reexamining The Death of Alan Turing

    Alan Turing, of Turing Test fame, would be 100 today. (Google has a clever animation to celebrate.) In conjunction with that anniversary, this story was posted which questions the usual story of his death: http://www.bbc.co.uk/news/science-environment-18561092
  37. X

    What's the difference between Turing Machine and UTM?

    1 - I'm trying to see what's the difference between a Turing Machine and a universal Turing Machine. Aren't the same? 2 - If I have a Touring Machine that to solve a problem, for example, adding numbers, what is the purpose of a Universal Touring Machine?
  38. X

    Turing machine - polynomial time expression

    In the Turing Machine, the machine accepts a word if the computation terminates in the accepting state. The language accepted by the machine, L(M), has associated an alphabet Δ and is defined by L(M) = {w \in \Delta} This means that the machine understands the word w if w belongs to the...
  39. C

    Turing Machines & Undecidability

    Homework Statement I have a question regarding undecidable languages. Let L1 = { M | M is an encoding of a Turing machine that accepts any input} and L2 = { M | M is an Turing machine with at most 100 states}. Is L1 intersect L2 decidable? Homework Equations The Attempt at a...
  40. J

    Assigning Godel Numbers to Turing Programs

    I am working through a computability theory textbook and right now the author is discussing assigning Godel numbers to each Turing Program. To do this, he suggests assigning each internal state, each of the elements of {1,B} and each of the elements of {L,R} a number. Then using these numbers...
  41. Loren Booda

    N-dimensional Universal Turing Machine?

    Can a Universal Turing Machine compute arbitrary, orthogonal sequences of integers in N dimensions for any N>0? Just an idea.
  42. W

    Troubleshooting X+y Turing Machine Example

    I am working out of Cutlands computability book and I am having trouble understanding the following example: "The function x+y is Turing-computable." Then the example lists the following specifications: q_1 1 B q_1 q_1 B R q_2 q_2 1 B q_3 q_2 B R q_2 I wanted to verify this worked...
  43. J

    Alan Turing and his homosexuality

    I remember I watched a documentary where they mentioned Alan Turing, a British logician, was considered a security risk once his homosexuality became open. I exactly remember they used the word "security risk". Why was he considered a security risk? I have been to Wikipedia and seems answers...
  44. R

    Trying to generate Turing patterns for Brusselator equations

    so my project is on reaction diffusion equations in 2d. i have been asked to reproduce known and published work to start off with and the system is the brusselator equations with diffusion terms. to put it simply my program doesn't work. now the parameter values for the equations are taken from...
  45. B

    Turing machine and quantum computers

    Can anyone help me...from Nielsen-Chuang "quantum computation and quantum information":how might we recognize that a process in nature computes a function not computable by a turing machine?
  46. B

    Turing machine, computable function.

    From Nielsen-Chuang:how might we recognize that a process in nature computes a function not computable by a turing machine?
  47. M

    Optimizing Turing Machine Functions: Finding the Minimum Cost and Enumeration

    Hello smart people, I am wondering if there is a process to convert a function to a Turing Machine. In other words, if I provide a list of input strings , and a corresponding output string for each input string, is there a way to find the minimum number of instructions to realize any function...
  48. T

    Programming Binary Addition with a Turing Machine

    hello, One can wonder what is the relation between the title of this thread and the subject of quantum mechanics, well, i was reading in a book about quantum computation and information and it was talking about computer science in some chapter where it shows a basic understanding of Turing...
  49. I

    Boolean expressions for Turing Machine

    Hello, I want to express Non-Deterministic Turing Machine constraint with boolean expression. The constraint is: "Cells which aren’t being read remain the same at time t+1". lets say H[i,j] means the read/write head at time i at cell j and S[i,j,k] means the symbol k at time i in cell j so the...
  50. daniel_i_l

    Can I Build a Mechanical Turing Machine Using Everyday Materials?

    As a summer project I was thinking of building an entirely mechanical Turing machine - possibly with Lego. Has anyone attempted this? Does anyone have any advice on how to design this? Thanks.
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