Questions tagged [turing-completeness]

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Explain the difference between Turing Complete and Turing Equivalence

I'm not sure if I understand the difference between Turing Complete and Turing Equivalent programming languages. A computational system that can compute every Turing-computable function is called ...
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0answers
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Is the While programming language with bounded number of variables Turing complete?

In our lecture it was proven that WHILE-Programs are turing-complete. In short a WHILE-Program only allows the following: ...
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1answer
41 views

Computation equivalence of functional and procedural programming

I'm really interested in the idea of functional programming, it seems like a very modular way of doings things. I've seen some suggestion that functional programming is just as powerful as procedural ...
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2answers
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Paradox? Pure Prolog is Turing-complete and yet incapable of expressing list intersection?

Pure Prolog (Prolog limited to Horn clauses only) is Turing-complete. In fact, a single Horn clause is enough for Turing-completeness. However, pure Prolog is incapable of expressing list intersection....
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1answer
41 views

What is the theoretical minimum number of “switches” requried to implement a Turing-complete CPU?

Where "switches" are the basic abstract building blocks for logic gates: vacuum tubes, transistors, magnetic relays, or whatever. We're not counting any switches in the RAM or tape drive ...
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1answer
438 views

Can a total programming language be Turing-complete?

I've seen two answers to this: Wikipedia says no: These restrictions mean that total functional programming is not Turing-complete. And the Wikipedia article cites D.A. Turner as the coiner of "...
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1answer
41 views

Is there a #$P$-complete counting problem such that every (valid) instance of its decision version is a Yes-instance?

I want to know whether there is a decision problem, written EasyProblem, satisfying the follow property: For every valid instance $x$, $x$ is a Yes-instance for EasyProblem (if we construct ...
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1answer
37 views

What is the computational class of a pushdown automaton with real values?

Say there is a push-down automata, in this example I'll use a deadfish-like set: +: increase x by 1 0: set x to 0 ...
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0answers
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How to map the tapes of a single tape Turing Machine into a “2-tape” Turing Machine which has only an initial state and an end state

so i am struggling with demonstrating that every single tape TM can be simulated by a 2 tape TM with only two states. I don't really understand how we can prof this with only 2 states.
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1answer
54 views

Universal Turing Machine algorithm

First, I learned this based on these facts: Turing machine (TM) will be define with 7-tuple Notation, $M=\langle Q,G,b,S,d,q_0,F\rangle$. Any computation rules that can use to simulate any possible ...
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2answers
117 views

Is there a query language variant of Turing Completeness?

By this I mean a theory where you can say Language X is Query Complete so that you know that language is able to do any sort of query? I'm guessing not because some queries would run into things that ...
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2answers
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Intuition for Church-Turing thesis for Turing machines

I can very clearly see "why" mu-recursion is a universal model of computation, i.e. why the Church-Turing thesis -- that any physically computable algorithm can be executed with mu-recursion ...
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3answers
266 views

Is English Turing-complete?

Is English Turing-complete? Intuitively it makes sense that English is Turing complete, since you can talk someone through building a Turing machine. But I also think there might be some operators ...
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1answer
45 views

Why is the Halting problem decidable for Goto languages limited on the highest value of constants and variables?

This is taken from an old exam of my university that I am using to prepare myself for the coming exam: Given is a language $\text{Goto}_{17}^c \subseteq \text{Goto}$. This language contains exactly ...
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1answer
58 views

Turing-completeness of Goto language with limited constants

This is taken from an old exam of my university that I am using to prepare myself for the coming exam: Given is a language $\text{Goto}_{17} \subseteq \text{Goto}$. This language includes exactly ...
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1answer
22 views

Determine if the following problem is decidable or not : Does the read–write head of a TM with the input w leave the word w?

Determine if the following problem is decidable or not : Does the read–write head of a TM with the given input w leave the word w on the tape?
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1answer
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Is the Languague which contains all TMs which write the blank symbol at firs by the given input w decidable?

Consider the problem of determining whether a Turing machine M on an input w writes the blank symbol at first. Is this decidable ?
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1answer
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Confusion in Turings proof of the undecidability of the Entscheidungsproblem

I was reading Turing's paper on computable numbers and the Entscheidungsproblem. There is this part of Section 9, Part II that I cannot quite seem to understand. He says: It is pretty straight ...
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2answers
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Equivalence between a TM and a changing TM

Let a changing TM be a TM which is not able to write the same symbol which is being read. Formal: $M^*=(Q,\Sigma,\Gamma,\delta,q_{accept},q_{reject})$,$\delta(q,a)=(q^*,a^*,c),a \neq a^*$ with $q,q^...
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1answer
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Lambda calculus without free variables is as strong as lambda calculus?

First question: How would one prove that by removing free (unbound) variables from lambda calculus, and allowing only bound variables, its power is not reduced (it is still Turing-complete) ? Second ...
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1answer
54 views

Turing machine that can move right only $O(1)$ steps beyond input

I need to prove that a Turing machine that can move only $k$ steps on the tape after the last latter of the input word is not equal to a normal Turning machine. My idea is that given a finite input ...
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0answers
47 views

If a turing machine can't solve the halting problem for a machine X, does this imply that X is at least as powerful as a turing machine?

Say I have a deterministic machine X, and I prove that a turing machine can't solve the halting problem for this machine when given a certain input. Does this imply that this machine X is turing-...
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Turing-completeness of affine programs

Are unguarded affine programs Turing-Complete? Are affine programs with affine guards Turing-Complete? Unguarded program: all branches are taken Affine program: only assignments like $x:=x_1+5x_2-...
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0answers
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Is there a recursive problem encoding the Turing completeness of a model of computation?

Suppose we have a model of computation $C$ we want to show to be Turing complete. The usual strategy would be to emulate within $C$ any model of computation we already know to be Turing complete (e.g. ...
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4answers
478 views

To what extent is an x86 machine equivalent to a Turing Machine?

To what extent is the abstract model of computation specified by the x86 language Turing complete? The above question is related to this question: Is C actually Turing-complete? In theoretical ...
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Is there defined limits on, how a Turing Machine can emulate itself / another one?

Meaning for example lower or upper bounds of any kind, possibly concerning time or space complexity?
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1answer
66 views

How can Turing complete machines exist theoretically if the halting problem is undecidable

As the question says, if I input on the tape of a Turing complete machine a program that solves the halting problem with the correct inputs the program will never end its execution regardless of ...
5
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1answer
306 views

How to write a coterminating, effectful program?

[Using Idris for code examples and terminology, but the question is not about Idris per se] In a post titled A Neighborhood of Infinity, @sigfpe argues that "the kind of open-ended loop we see in ...
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2answers
250 views

What can't you do without Turing-completeness?

I suppose that, since a Turing-complete language can simulate a Turing-machine, a non-Turing-complete language can't, but most programs do not have the simulation of a Turing machine as their purpose. ...
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Is the language “untyped arithmetic expressions” in Types and Programming Languages not Turing complete?

In Types and Programming Languages by Pierce, is it correct that the language introduced in Chapter 3 Untyped Arithmetic Expressions is not Turing complete? Because it doesn't provide recursion. the ...
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1answer
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Number of logic gates for “reasonable” Turing completeness

Somewhere on stackexchage, I, or someone else asked what was the proper term for Turing completeness minus the infinite memory (e.g. a Turing machine that one can actually build, no bigger than your ...
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I've proven my language undecidable what is left to prove it Turing equivalent?

Let us say that I have a computation model $A$. Let us also say that I have shown that $A$ can be simulated by a Turing machine. I have not been able to prove that $A$ can simulate a Turing machine. ...
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1answer
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Is the infinite program Turing-recognizable/decidable?

Imagine we have a program which does an infinite loop: while(true){loop} We run the program on a linux machine(assume the compilation is ok), then this linux ...
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1answer
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If the human brain is a Turing machine then how is it able to ascertain that certain problems are undecidable? [closed]

I recently read about the idea that the human brain might be a Turing machine (or Turing complete). If that is true then how is the brain able to reason that a certain problem is undecidable for e.g. ...
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1answer
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Prove completeness of a language with Turing Machine

I'm trying to prove that a simple computer language is Turing Complete. For that, I did some researches about Turing Machine and I found (if I understand correctly), that we can prove that by simuling ...
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4answers
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Are Finite Automata Turing Complete?

Something is Turing Complete if it can be used to simulate any Turing Machine. So, can a Finite Automaton simulate a Turing Machine? On the question Can regular languages be Turing complete? they ...
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2answers
99 views

Are Linear Bounded Automatons Turing Complete?

Linear Bounded Automatons are just Turing Machines with finite tape, instead of infinite tape. But this causes them to not be Turing Complete? Why?
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1answer
91 views

What are the benefits of languages that are not Turing complete?

Unfortunately I did a degree in CS without much theoretical computer science. One thing I used to hear is that sub languages, or languages which are not Turing complete, allow for better optimization? ...
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1answer
45 views

Uncomputably coded model of computation

There are many different but equivalent models of computation. I assume their equivalence is shown by coding input of one model to the input of the other model and making an argument why should there ...
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246 views

Are Context Sensitive Languages Turing Complete? [duplicate]

Related questions: Can regular languages be Turing complete? Why are Linearly Bounded Turing Machines more powerful than Finite State Automata? https://stackoverflow.com/questions/14589346/is-c-...
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Proving Turing Completeness by creating a compiler to a Turing Complete language

Given a programming language A unknown to be Turing Complete, if one can create a compiler for a TC programming language B using A does this imply that A is itself Turing Complete? If so, what is the ...
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2answers
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Can a language with some set of higher-order functions like map, fold and filter but without recursion or iteration be Turing complete?

I was reading this article and was wondering if there is any finite set of higher-order functions like map, fold or filter such that they could empower a language to be Turing complete even without ...
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1answer
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Is turing completeness related to recursive enumerable languages?

I recently came across this term "Turing complete" in my study of morphogenesis models. When I looked up, it said that a turing complete machine can simulate a universal turing machine. When I ...
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Unbounded-time programs in lambda calculus?

The Turing machine model has been extended to “infinitary turing machines”, which are Turing machines that can perform a countably and uncountably infinite amount of computations in finite time. Is ...
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Is C actually turing complete follow up [duplicate]

I am picking up from this thread for which I have no privileges to comment on: Is C actually Turing-complete? I was wondering if there's any progress on this and what the conclusion actually was. ...
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2answers
451 views

Is arithmetic turing complete?

Maybe my question doesn't make sense, because I lack some more thorough understanding, but I was curious if arithmetic was Turing complete? As I understand it, a "model of computation" is a mechanism ...
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If only using bit-shifts can produce a Turing-machine, or if you need more bitwise operations

So you can have One Instruction Set Computers. But typically these instructions have rather complicated underlying implementations. addition (addleq, add and branch if less than or equal to zero) ...
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Automata that is Turing complete if you add a nondeterminism

Pushdown automata have an interesting property: non-deterministic ones belong to a different computational class than deterministic ones. This is in contrast to finite state and turing machines, for ...
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1answer
108 views

Can one get Turing-completeness without nontermination?

As I'm reading the movfuscator paper by Stephen Dolan, I encounter this claim: In order to have Turing-completeness, we must allow for nontermination. This seems like a reasonable statement. But I'...
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Computability of Kolmogorov complexity in total languages

It is well known that the Kolmogorov complexity is uncomputable in Turing-complete programming languages. However, what about total programming languages? For example, is the Kolmogorov complexity of ...