Programming Binary Addition with a Turing Machine

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Discussion Overview

The discussion revolves around programming binary addition using a Turing machine, specifically focusing on how to add two binary numbers modulo two with constraints such as a single tape and one read/write head. The conversation also touches on the relevance of Turing machines to quantum mechanics and the distinction between standard and universal Turing machines.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to write a program for binary addition using a Turing machine with specific constraints, expressing curiosity about its feasibility.
  • Another participant discusses the various definitions of a universal Turing machine and suggests that the task may be more of a curiosity with pedagogical value, while questioning its relevance to quantum mechanics.
  • A different participant notes their confusion about the difference between "standard" and "universal" Turing machines, indicating they are new to the topic.
  • Some participants express a desire to understand the connection between Turing machines and quantum computation, reiterating the relevance of the discussion to quantum mechanics.
  • Links to external resources are provided by participants to aid understanding of Turing machines.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of Turing machines to quantum mechanics, and there is no consensus on the best approach to programming binary addition with the specified constraints. The distinction between standard and universal Turing machines also remains a point of confusion.

Contextual Notes

Participants mention the use of one tape with two heads as a potential alternative, but the implications of this approach are not fully explored. There are also unresolved questions regarding the definitions and characteristics of standard versus universal Turing machines.

Who May Find This Useful

This discussion may be useful for those interested in the intersection of computer science and quantum mechanics, particularly in understanding Turing machines and their applications in computational theory.

theophyman
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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 machine.
Ok, my question is: how to write a program that adds (modulo two) two binary numbers (assuming that they have the same length) separated by a 'blank' . the turing machine has only one tape and one read/write head.

is it possible?

thank you
 
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There are many equivalent definition of what a universal Turing machine is, it could have just one tape, or several. In fact, anything a computer can do, a Turing machine can do as well. The rule of the game is to start from something as rudimentary as possible and progressively build up complexity. Quite frankly, I believe writing such a program is more of a curiosity, possibly with pedagogical value, but again : how is this relevant to quantum mechanics ?
 
humanino said:
There are many equivalent definition of what a universal Turing machine is, it could have just one tape, or several.

i am new in learning Turing machines, but i think there is a difference between "standard" turing machine and universal turing machine. my question is about the "standard" one.


humanino said:
I believe writing such a program is more of a curiosity, possibly with pedagogical value, but again : how is this relevant to quantum mechanics ?

i can get the answer of my question using one tape with tow heads (is it acceptable?).

humanino said:
how is this relevant to quantum mechanics ?

as i said in my question above, i am learning quantum computation and quantum information,i found the turing machine and universal turing machine in a book about the subject of quantum computation and information.
 
Found this for ya. Hope it helps your understanding.

http://www.maths.leeds.ac.uk/~awmorp/turingmachine/turing.html
 
Last edited by a moderator:
mikestampone said:
Found this for ya. Hope it helps your understanding.

http://www.maths.leeds.ac.uk/~awmorp/turingmachine/turing.html

thank you, it was very helpful.
 
Last edited by a moderator:

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