# Questions tagged [turing-completeness]

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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 ...
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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: ...
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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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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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 ($2^{n + 1}$) ...
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### 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 ...
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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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### 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....
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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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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