# Questions tagged [turing-completeness]

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### Does a language/maschine/system need to be able to halt to be universal?

Is it possible for a language (or machine or system) to be universal or turing complete, when there is no possibility to write a program for it that halts? Lets say we create a new language, brainfuck-...
1 vote
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### Can we ever achieve Turing completeness?

I want to relate Turing completeness to the Halting Problem. As far as I know we say something is turing complete (eg: a programming language) when it can compute any function and can do any task. But ...
287 views

### Does the first incompleteness theorem imply that any Turing complete programming language must have undefined behavior?

If I understand correctly, the first incompleteness theorem says that any "effectively axiomatized" formal system which is consistent must contain theorems which are independent of the ...
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### What are quines (layman friendly)?

I was going through the Wikipedia page on Quines and did not understand this paragraph - A quine is a fixed point of an execution environment, when the execution environment is viewed as a function ...
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### Is a machine Turing-complete when it can decide a context-sensitive language?

If a machine can decide a context-sensitive language (like the language of palindromes with a non-linear center) is that fact a proof that the machine is Turing-complete? Can this be used to prove ...
4k views

### Does the Turing test have anything to do with Turing completeness or Turing machines?

I am studying Turing machines and Turing completeness and just remembered I saw something called the Turing test. It seems that the Turing test (from Wikipedia) is a test of a machine's ability to ...
1 vote
34 views

### Concrete example of a set with a lower degree of unsolvability

Post's problem, posed in 1944 by Post, was to know if there is a recursively enumerable set, which, being undecidable, was not equivalent to the Halting problem under Turing reducibility. While I've ...
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### Why, in principle, can a Turing machine describe any computation or procedure?

Why is it that a Turing machine can perform all kinds of calculations and procedures? As a test, I tried to perform a four-quadratic calculation using a Turing machine myself. However, although I ...
252 views

### Is DNA computation Turing complete?

I have heard DNA being referred to as "code", this is because it is an instruction set which dictates the bodies' properties. However, DNA (as far as I have learned), has no conditional ...
66 views

### If a Turing machine can compute any computable problem how can Turing completeness be achived?

To my knowledge a Turing machine is able to compute anything considered computable. I got the definition of Turing completeness from this answer Explain the difference between Turing Complete and ...
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### Is Brainf*ck still Turing Complete without I/O?

I've made an interetsing esolang, and to prove Turing completeness, I've written a small Brainf*ck interpreter in it. However, due to the nature of the language, input is rather hard to handle. The ...
1 vote
87 views

### Why is the Church-Turing thesis not accepted as fact?

I recognize that it has overwhelming consensus at this point, but from what I understand, it's still technically considered "probably true" instead of "definitely true". If we go ...
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### Why is Rule 110 considered "weakly" universal?

My supposition is that this is was more or less an automatic designation based on the fact that Rule 110 requires an infinite "background tiling" of the 14-bit sequence ...
1 vote
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### Instances of simulating lambda calculus?

There are a ton of resources on the web devoted to proving some esoteric language is Turing complete by simulating arbitrary turing machines. I have an esoteric language I want to prove is complete, ...
1 vote
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### The simplest Turing-complete language

To prove that a new language is Turing-complete the authors need to show that it can simulate any other (already known) Turing-complete language. I wonder what Turing-complete language is the simplest ...
1 vote
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### Simple proof that Lisp expresses all computable list functions

Given computable function $f : LispTerm \rightarrow LispTerm$ is it possible to implement it in Lisp? The $LispTerm$ is any term that is constructed using cons, <...
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### Is Turing completeness necessary?

Most programming languages are Turing complete (finite memory blah blah blah), and when we design languages this is a goal. But is it really necessary? What algorithms do we typically use that require ...
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### How does nondeterminism affect the power of a machine?

For example, in finite-state machines (FSM), the main difference between a deterministic (DFA) and a non-deterministic machine (NFA) is that there are possibly more branches or outputs for each input, ...
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### What exactly does Turing Equivalence mean?

Assume I have a programming language $L$ with well-defined semantics. Showing Turing-completeness is straightforward: if I write a program using $L$ simulating the universal TM, I'm done. What I'm ...
1 vote
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### What are practical applications for markovs algorithm(string rewriting systems)

:) Currently I am browsing through the internet on the hunt for a topic for my bachelors thesis. Whilst being on Reddit I discovered an interesting repo (https://github.com/mxgmn/MarkovJunior) for a ...
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### What is the most computationally efficient Turing complete system?

I'm making a program that involves making models of and working with arbitrary systems (or programs). What is the most computationally efficient Turing complete system to model these in? By "...
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### What does it mean for a machine language to be Turing-complete?

I was reading the Wikipedia article on Turing completeness, but I was having a hard time putting together all of the concepts. In simple terms, what does it mean for an instruction set to have Turing-...
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### How could you encode such a function in lambda calculus?

I just read the definition of lambda calculus. Apparently it's Turing complete, but I tried writing a very simple function and I couldn't: ...
1 vote
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### In a rigorous mathematical sense, what is the significance of Turing-completeness?

I know that Turing-completeness is the ability to simulate a Turing machine, and from what I've read, the reason why we should care about Turing-completeness is that it demonstrates that a machine can ...
1 vote
118 views

### kolmogorov complexity for finite Language?

In lectures my professor proved that there is no Turing machine that for every x it calculates k(x). On the other hand, I saw a claim online that for finite language L there is a Turing machine that ...
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### Finite Number of Turing Machines that stop after k steps?

For this question suppose Alphabet for input is {0,1}. Given: L={<M> | M stops on every input after maximum 1000 steps} My professor claimed that there is a ...
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### Is the set of all halting programs for all universal Turing machines recursively enumerable?

I understand that one can use dovetailing to recursively enumerate the domain of a UTM. However, I am trying to recursively enumerate the domain of all possible UTM. My starting point was to use a ...
3k views

### How Turing Machine Can Never Stop?

My professor discussed the following Turing machine M' on input (,x): Generate number n Run M on X, for n steps If M stops, accept I don't understand No.3 If we are running M on input X for final ...
1 vote
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### Are all Turing machines Turing complete?

I have recently been reading up on TOC, and had this thought, which does not seem to be answered explicitly anywhere. They way I have understood it, a system is Turing complete if it can simulate any ...
3k views

### Can any known sub-Turing-complete model of computation enumerate precisely the set of prime numbers?

I wish there were more, but the subject pretty much captures my whole question. Is there a non-Turing-complete model (some constrained term rewriting system or automaton or what have you) which is ...
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### Are there infinitely many distinct implementations of any algorithm using any Turing-complete computational model?

Subject pretty much says it all. My strong impression is that for any algorithm and any choice of programming language or computational model, if it's Turing-complete, then there must be infinitely ...
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### Is Desmos Turing-Complete?

The graphing calculator Desmos has a ton of functions, and can express any arithmetric formula. What I want to know is, is it Turing-Complete? Desmos supports, among other things: Most mathematical ...
1 vote
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### Had Conway's Game of Life or any C-A been demonstrated to generate non-repeating pattern?

As we know, Conway's Game of Life is Turing-complete. And Turing-complete systems can be used to calculate irrational numbers such as $\sqrt{2}$, $\pi$, $e$, etc. which have non-repeating digits. So ...
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### Necessity of encoding for certain models of computation

Consider the following model of computation (from here). Although Fractran is Turing-complete, it assumes that the "user" is able to perform the steps of encoding the input ($2^{n + 1}$) ...
108 views

### how can turing machines be universal models of computation if they can't perform binary search?

I have searched around and it seems like it is impossible for a Turing machine to implement binary search for an arbitrary sized array. How can a turing machine be called universally computable if it ...
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### How do we define the term "computation" across models of computation?

How do we define the term computation / computable function generically across models of computation? Beginning with the textbook definitions of: {Linz, Sipser and Kozen} for "computable function&...
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### EQ_{TM} is not Turing recognizable, but we can reduce A_{TM} to it?

So as I understand $EQ_{TM}$ (problem of deceiding whether two turing machines are equivalent) is not Turing Recognizable (by showing that $A_{TM}$ is reducible to its complement ${NEQ_{TM}}$). But we ...
914 views

### 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 ...
263 views

### 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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### 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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### 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....
1 vote
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### 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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### 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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### 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 ...
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 ...