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Questions tagged [turing-machines]

Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

The classic paper that started it all.

On Computable Numbers, with an application to the Entscheidungsproblem

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Why is the Turing Machine a popular model of computation?

I am a CS undergraduate. I understand how Turing came up with his abstract machine (modeling a person doing a computation), but it seems to me to be an awkward, inelegant abstraction. Why do we consider a "tape", and a machine head writing symbols,…
Alex
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Are there minimum criteria for a programming language being Turing complete?

Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete? From what I can tell from wikipedia, the language needs to support recursion, or, seemingly, must be able to run…
Khanzor
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Human computing power: Can humans decide the halting problem on Turing Machines?

We know the halting problem (on Turing Machines) is undecidable for Turing Machines. Is there some research into how well the human mind can deal with this problem, possibly aided by Turing Machines or general purpose computers? Note: Obviously, in…
bitmask
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Is a Turing Machine "by definition" the most powerful machine?

I agree that a Turing Machine can do "all possible mathematical problems". But that is because it is just a machine representation of an algorithm: first do this, then do that, finally output that. I mean anything that is solvable can be…
Sounak Bhattacharya
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How to define quantum Turing machines?

In quantum computation, what is the equivalent model of a Turing machine? It is quite clear to me how quantum circuits can be constructed out of quantum gates, but how can we define a quantum Turing machine (QTM) that can actually benefit from…
Ran G.
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Is a push-down automaton with two stacks equivalent to a turing machine?

In this answer it is mentioned A regular language can be recognized by a finite automaton. A context-free language requires a stack, and a context sensitive language requires two stacks (which is equivalent to saying it requires a full Turing…
Lazer
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Theoretical machines which are more powerful than Turing machines

Are there any theoretical machines which exceed Turing machines capability in at least some areas?
user1561358
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Difference between a turing machine and a finite state machine?

I am doing a presentation about Turing machines and I wanted to give some background on FSM's before introducing Turing Machines. Problem is, I really don't know what is VERY different from one another. Here's what I know it's different: FSM has…
Julio Garcia
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why don't we use machines with random access memory as our basic model of computation?

Turing machines are perhaps the most popular model of computation for theoretical computer science. Turing machines don't have random access memory, since we can only do a read where the slider is currently located. This seem unwieldy to me. Why…
user56834
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What is the difference between quantum TM and nondetermistic TM?

I was going through the discussion on the question How to define quantum Turing machines? and I feel that quantum TM and nondetermistic TM are one and the same. The answers to the other question do not touch on that. Are these two models one and the…
bongubj
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What does being Turing complete mean?

I see that most definitions of what it is to be Turing-complete are tautological to a degree. For example if you Google "what does being Turing complete mean", you get: A computer is Turing complete if it can solve any problem that a Turing machine…
sashoalm
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What are the simplest examples of programs that we do not know whether they terminate?

The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. What are the simplest (smallest) known examples of…
MaiaVictor
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Why are there more non-computable functions than computable ones?

I'm currently reading a book in algorithms and complexity. At the moment I'm, reading about computable and non-computable functions, and my book states that there are many more functions that are non-computable than computable, in fact the majority…
hsalin
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Practical importance of Turing machines?

I am an electrical engineer, and only had one CS course in college 26 years ago. However, I am also a devoted Mathematica user. I have the sense that Turing Machines are very important in computer science. Is the importance only in the theory of…
Ted Ersek
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Is there a connection between the halting problem and thermodynamic entropy?

Alan Turing proposed a model for a machine (the Turing Machine, TM) which computes (numbers, functions, etc.) and proved the Halting Theorem. A TM is an abstract concept of a machine (or engine if you like). The Halting Theorem is an impossibility…
Nikos M.
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