Questions tagged [turing-completeness]

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1answer
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Is There a Complete Problem for the Class of Turing Decidable Problems?

Languages such as $\text{HALT}_{TM}$ are $\textsf{RE-complete}$ under many-one reductions. It is trivial to see that $\text{co-RE}$ has complete problems, too. S. Schmitz [1] considers some classes ...
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1answer
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Given a λ-term, can I decide which machine model I need to express it?

I am having a hard time figuring out the specific relationship, of various things in computability. So we have a hierarchy of machines, with a (real life) upper bound of Turing machines, moving on ...
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0answers
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What language features would I need to remove from a real programming language to make it decidable? [closed]

Let's say that I want to restrict certain features of a common programming language--for instance, C--such that the result is decidable, and thus no longer Turing-complete. What language features, at ...
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1answer
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Simplest Turing-complete ruleset for Markov algorithm

Is there an example of a particular ruleset for a Markov algorithm that is Turing-complete? If so, what is the simplest example of such a ruleset?
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Computational power of Actor Model

In the question below, let TM be Turing machine, NTM be nondeterministic Turing machine and PTM be probabilistic Turing machine. In his paper "Actor Model of Computation: Scalable Robust Information ...
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2answers
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Which calculus is based on first-order functions and is Turing complete?

Which calculus is based on first-order functions and is Turing complete? I know of calculi which are Turing complete, but based on higher-order functions: Lambda calculus SKI combinator calculus ...
5
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1answer
295 views

How rule 110 would be proven to be universal if the tag system did not exist?

I was reading about Cellular Automata and I read in this question that Matthew Cook proved that rule 110 is universal, and that his proof relied upon showing how rule 110 can simulate a tag system. ...
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3answers
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Is there an algorithm for converting Turing machines into equivalent Lambda expressions?

We know that Turing machines and Lambda Calculus are equivalent in power. And There are proofs for that, I'm sure. But is there an algorithm, a systematic way for us to convert a Turing machine into ...
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2answers
295 views

Is a language with only a stack of fixed-size integers Turing-complete?

I encountered the brainfuck programming language which I know is turing complete. However I then decided to create a high level language that gets compiled to brainfuck code. There is only one data ...
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5answers
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Is there any example of automatas (or similar) systems that emerge complex internal structures on its own?

Automatas are turing-complete grid-based systems with progression rules on which we can encode arbitrarily complex structures. For example, this is a "glider gun" on Conway's Game of Life: Due to ...
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1answer
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FSM + state data is Turing complete abstraction?

I'm playing with Akka FSM. The declaration of a an Akka FSM consists of states + data mantained during the states (the akka doc is more clear than me) + events that trigger transitions between states. ...
5
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1answer
141 views

Can a language be Turing Complete if its only provision for unlimited code/memory is through recursion?

We've developed an esoteric language. In this language, a program contains a static amount of code, and a static amount of storage space. However, parts of the program can recurse, so the interpreter ...
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4answers
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Do we need recursion in programming language to solve any problem?

My question is simple: If we want to be able to solve every problem, that we can solve using recursions, do we need programming language to allow us use recursions? Assuming we are allowed to use: ...
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4answers
2k views

What is required for universal analogue computation?

What operations need to be performed in order to do any arbitrary analogue computation? Would addition, subtraction, multiplication and division be sufficient? Also, does anyone know exactly what ...
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1answer
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How can a universal Turing machine simulate “bigger” ones?

I'm trying to find the answers of two questions about the Universal Turing machine. How can the Universal Turing machine simulate a Turing machine if the one that is being simulated has a bigger ...
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2answers
771 views

Is a stack machine with a forward read iterator Turing complete?

It is well known that a machine with a single stack as only unlimited storage is not Turing complete, if it can only read from the top of the stack. I want a machine which is (slightly) more powerful ...
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4answers
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Can we write algorithms without conditional statements?

Regarding turing completeness, i read that for a language/machine to be turing complete it is required that it has some sort of conditional. Consider the factorial problem, we would typically define ...
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1answer
842 views

Does stay put TM recognizes same languages as standard TM

I am reading this text book and it says that stay put turing machine recognizes the same languages as regular turing machine by just adding transition functions (without adding any new states or ...
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1answer
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How close are common programming languages to not being Turing complete?

The term "Turing completeness" has been discussed in several of the Computer Science classes that I've taken. However, I've never gotten an intuitive feel for what Turing completeness actually ...
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2answers
375 views

Finite number of Turing machines running concurrently on multi-tapes Turing-machine-equivalent?

So basically, there are several (finite number of) Turing machines being able to read off and write to the same set of tapes (the number of tapes is finite, but each tape may have infinite tape spaces)...
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1answer
132 views

Are conditionals necessary in computation? [duplicate]

I know this question might seem weird, maybe I'm just overthinking, but this is really troubling me because I've been a computer engineer for some time now and conditionals (if statements for instance)...
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3answers
745 views

Rice's theorem vs Turing completeness

I would like to clarify this because I see some kind of contradiction between Rice's theorem and Turing completeness. This is the problem: In building an Universal Turing Machine to emulate another ...
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1answer
717 views

Is model theory useful for computer scientists

It is often stated in the CS folklore that Turing was inspired by Gödel's incompleteness theorem, more specifically the diagonalization proof and the isomorphism between axiomatically generated ...
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1answer
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Two functions which can create any computable function by composing?

Do there exist two computable functions, a and b, which can construct every computable function by a finite serie of a's and b's which is function composed? Fx. let's take the serie, a,b,a,b,b,a,a,a , ...
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2answers
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Are Boolean functions Turing complete

A Boolean function is a function $f:\{0,1\}^n\rightarrow\{0,1\}$. The boolean basis $(\vee,\wedge)$ is known to be Turing complete as it allows any sequence $s\in\{0,1\}$ to be flipped or to be left ...
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0answers
527 views

How to simulate a cellular automaton via a Turing machine

It is rather easy to see that every cellular automaton can be simulated by a Turing machine: We can simulate a cellular automaton with an appropriate C program and every C program can be simulated by ...
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2answers
669 views

Do Higher Order Functions provide more power to Functional Programming?

I've asked a similar question on cstheory.SE. According to this answer on Stackoverflow there is an algorithm that on a non-lazy pure functional programming language has an $\Omega(n \log n)$ ...
4
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1answer
327 views

Is a Turing Machine that only takes strings of the form $0^*$ Turing Complete?

You have a Turing machine that only processes input on the form $0^*$. If it is given an input without 0's, it will simply halt without accepting or do anything else. Is it Turing Complete? The set $...
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2answers
380 views

If a DFA can be simulated by a real program, can it be simulated by a TM

In proofs of decidability, we often want to simulate another model of computation by a Turing machine. But if I can simulate a $\mathsf{DFA}$ by, say, a C program, then is there some result which says ...
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1answer
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Simulating a TM with a 2-head, right moving TM

Is it possible to simulate a regular Turing Machine with a TM with the following specs? There are two heads, one of which can read, one of which can write Both heads can only move right When a head ...
2
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1answer
422 views

Would adding recursive named functions to Simply typed lambda calculus make it Turing complete?

Say I have Simply typed lambda calculus, and add an assignment rule: <identifier> : <type> = <abstraction> Where ...
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0answers
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On the Turing Completeness of First Order Logic

It is well known that in Descriptive Complexity Theory FO is equivalent to AC0. However, this accepts a couple of a theory and a string <T,s> iff the ...
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1answer
307 views

How do you say when a language is Turing-complete only in a trivial way?

I didn't know how to ask this question before but now that I'm reading about typed lambda calculus I think I've got a better idea. There is this answer to a question asking whether CSS is Turing ...
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2answers
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Does a Universal Turing Machine have more computational power than a non-universal one?

I'm a bit confused about these concepts. As far as I understand, something is Turing complete when it can simulate a Turing machine. And there is this thing called a Universal Turing machine which is ...
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2answers
3k views

Clear, complete, proof that a language is Turing Compete?

I have seen web sites that purport to "prove" that HTML5+CSS is Turing Complete. I have seen web sites that purport to "prove" that SQL is Turing Complete. I have seen a bunch of web sites that ...
0
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1answer
791 views

Class of the language of Turing machines that loop on at least one input

$L = \{ \langle M \rangle \mid \text{there is at least one input string on which the \(M\) does not halt} \}$ Here, for a Turing machine $M$, the notation $\langle M \rangle$ denotes an encoding, ...
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2answers
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Can a method be written if the language is undecidable?

If a language is decidable, we can write a method that always halts and returns true for each string that is an element of the language and ...
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0answers
130 views

Make a tag system simulate a finite automaton?

Tag systems are Turing-complete. I was wondering if there is any easy way to create tag systems that simulate finite automata. So create tag systems that recognize languages, e.g. by having at the end ...
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1answer
501 views

Is it possible to write a universal loop program for if-then & loop programs and it is possible to write a universal while program for while progra

Is it possible to write a universal loop program for if-then & loop programs and it is possible to write a universal while program for while programs? Long version and some background: Before ...
4
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1answer
260 views

Natural RE undecidable problems but not Turing-complete

The Halting problem is a natural undecidable language which is complete for the set of recursivly enumrable sets. I am interested in undecidable but not Turing-complete language such that we can not ...
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3answers
156 views

Looking for some more details on “Turing” devices

I've been reading a lot of computer science literature in the recent past but haven't ran across an explanation of Turing machines, the different types, and why they seem to come up so often (I ...
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1answer
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To prove Turing-completeness, is it enough to prove capability of producing arbitrary output?

Turing completness is being typically proved via reduction to already proved Turing-complete machine. Can the same be obtained by showing, that the machine in question is capable of generating ...
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3answers
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What are the minimum requirements for a language to be considered Turing Complete? [duplicate]

Possible Duplicate: Are there minimum criteria for a programming language being Turing complete? I overheard a conversation on the topic and the conclusion that one gent came to was that in order ...
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4answers
525 views

Is a device with restrictive execution policies Turing-complete?

There are devices that do not allow users to load any application they want on it, only run a limited class of applications approved by the device vendor. Take an iPhone as an example where new ...
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2answers
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Universality of the Toffoli gate

Regarding the quantum Toffoli gate: is it classicaly universal, and if so, why? is it quantumly universal, and why?

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