Questions tagged [turing-completeness]

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If the human brain is a Turing machine then how is it able to ascertain that certain problems are undecidable?

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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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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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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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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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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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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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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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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Does a Turing complete set of invertible combinators exist?

We'll say that a combinator A is invertible if there exists A' s.t. A'(Ax) = A(A'x) = x For example, Sxyz = xz(yz) is clearly invertible in this sense because we ...
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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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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 ...
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Does undecidability violate Turing completeness? Shouldn't “complete” include “decidability”? [closed]

Does undecidability violate Turing completeness? Shouldn't "complete" include "decidability"? That is, if one has a language that's Turing complete, but expresses infinite computation (i.e. may not ...
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How many pairs of brackets are sufficient to make Brainfuck Turing complete?

Brainfuck is a Turing complete programming language that uses only 8 symbols (6 if you ignore I/O). The two most notable ones that push it to Turing completeness are ...
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Halting problem of TM which recognize recursive languages is undecidable?

I am preparing for an exam and I came across this question in one of the tests. Halting problem of Turing machines which recognize recursive languages is undecidable. (True / False) The solution ...
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Weaker, but similar conditions to Turing completeness?

A model of computation is called Turing complete if it can simulate any Turing machine. This rules out for example a combinational logic circuit. However, there is a sense in which combinational ...
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Is this system Turing complete?

I want to develop a genetic program that can solve generic problems like surviving in a computer game. Since this is for fun/education I do not want to use existing libraries. I came up with the ...
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What is the simplest/smallest subset an OOP language like C#/JavaScript that is Turing-complete?

This question is not meant to be too theoretical or nitpicky. I have experience programming, so I'm trying to get a better understanding of what it takes to get Turing-completeness by using my ...
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Can PDA model Turing Complete objects if the objects' state are finite?

I am currently reading the extended Version of the Paper Online Detection of Effectively Callback Free Objects with Applications of Smart Contract. I am trying to understand the proofs of Chapter 6. ...
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Why does Turing Tumble need gear bits to be turing complete?

I understand intuitively that gear bits in the massively successful Turing Tumble game (funded by kickstarter) are necessary for Turing completeness*. I had a fantasy about building a computer with ...
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1answer
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Obtain all possible Turing Machines from a Universal Turing Machine

Knowing how a Universal Turing Machines works and its capabilities, is it possible to obtain the collection M = {M0 , M1 , M2 , M3, … } of all possible Turing Machines? If so, can we prove that a ...
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How can a 64KiB computer do the same task as a modern computer?

I took an extremely interesting intro to CE course, learning about transistors/memory/logic gates up to LC-3 assembly. Something that was really interesting to me was learning about how a processor's ...
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Transport Triggered CPU Architecture MOV and Turing Completeness

Reading up on TTA CPU designs and the wikipedia article states that Some TTA implementations support conditional execution. The trick to make an TTA ISA Turing-complete with an unconditional MOV ...
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1answer
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How to compute (x MOD y) with just SUM and MULT gates?

It is known that $\{ SUM, MULT \}$ is Turing-complete, i.e. every Turing machine has an equivalent circuit made up of $SUM$ and $MULT$ gates. By the way, I could not come up with designing $MOD$ ...
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Are all turing complete languages interchangeable

Note, while I know how to program, I'm quite a beginner at CS theory. According to this answer Turing completeness is an abstract concept of computability. If a language is Turing complete, then ...
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Is it possible to have a code which cannot be solved by computer

I was looking at Turing machines and Turing completeness and I was wondering whether it is possible to prove that there is a problem which cannot be solved by a Turing complete computer or whether it ...
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Emergent complexity and Turing Completeness

Is there some link between the concept of emergence and Turing Completeness? The ideas feel intuitively like they might be linked, but I can find nothing online. The idea came to me because I was ...
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In what sense can a cellular automaton be Turing complete? [duplicate]

The rule 110 cellular automaton is known (or claimed) to be Turing complete. But what exactly does it mean? I do know what Turing completeness mean. Roughly speaking a language is Turing complete if ...
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Infinite Boolean circuits as a model of computation

Boolean circuits are non-uniform models of computation in that they require a different circuit for each length of input. The typical way of uniformizing a family of Boolean circuits is to define a ...
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1answer
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How is PowerPoint Turing complete?

From my understanding, Turing complete means that the program or machine can complete any computation that a Turing machine can complete, which to me means any computation. So how can something like ...
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1answer
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What was the first Turing-Complete programming language?

What was the first turing-complete language? Know about the first machines and computers, but not the programming language.
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Is there a dual concept to “Turing Complete” in logic?

Two computing models can be shown to be co complete if each can encode a universal simulator for the other. Two logics can be shown to be co complete if an encoding of the rules of inferences (and ...
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1answer
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Who was the first to show that there is a Universal Turing-Machine that uses a binary alphabet?

The title says it all, I think. We know there are universal Turing-machines that only use a binary alphabet. But who proved this first? Turing himself showed the existence of a universal Turing ...
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Is the ability to do depth first search a proof of Turing Completeness? Can we write a non-TC automaton that does DFS?

As the title states. Let's say we have a set of inputs that define a tree structure. Is it possible to construct an automaton that can perform depth-first search on this data that is not Turing-...
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Turing-completeness, Conway's Game of Life and Logical Gates

I was recently given an assignment at university asking me to discuss the universal computational capability of Conway's Game of Life. I'm not required to actually build up a Universal Turing machine ...
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Is there a problem solution which, if implementable in a given language, implies that that language is Turing complete?

I have been researching a bit lately and found myself thinking about the title question for some time now, but have found nothing conclusive. For example, some problems require loops practically - ...
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What portion of all possible turing machines halt?

Has anyone estimated Chaitin's constant for Turing machines with an empty tape as input?
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Is a reduced Wang B-machine Turing-complete?

A Wang B-machine has only 4 instructions: right: Move tape head right left: Move tape head left ...
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Find the odd shortest path is NL

OddPath be a set of all G, s, t, such that G is a directed graph with a path from node s to node t, and the shortest such path has odd number of edges. How can I show OddPath is NL? I think about it ...
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Lambda Calculus in Rewriting systems

How to do or implement Lambda Calculus in a Rewriting systems? Rewriting systems are Turing complete. But I can't figure out how to do lambda calculus or functions with them.
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How many gates until Turing Complete

A computer can be pretty much made using just nand gates and a clock. Suppose you randomly place down nand gates on a board and connect them randomly to other nand gates. How many gates does someone ...
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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 ...
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Looping and branching with Algorithmic Differentiation

Algorithmic (aka Automatic) Differentiation is a wonderful technique for numerical computation of derivatives. I understand how it relates to the fact that we know how to deal with every elementary ...
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Is learned RNN still universal?

I know it has been shown that RNNs are Turing complete. So for any Turing machine, there exists a configuration of a RNN that is equivalent to it. But I'm wondering, is all those configuration ...