Questions tagged [church-turing-thesis]

For questions about the interpretation, extension and validity of the Church-Turing thesis, the hypothesis that states that a function is effectively calculable by a human if and only if the function is computable (on a Turing machine)

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What is the difference between the Church-Turing thesis and the Church-Turing-Deutsch principle?

I am trying to get a better handle on the Church-Turing thesis, and I am confused by the difference between the two ideas in the title. The wikipedia page for the Church-Turing thesis says, the ...
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How to show that the set of all turing machines that halt on a blank tape form a recursively enumerable set

I learned in my class that set of all Turing machines that halt on a blank tape form a recursively enumerable set. I was told that you can prove it using an argument similar to the diagonalization ...
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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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Does Nondeterministic TM is a counterexample of Extended Church-Turing Thesis?

We know that Extended Church-Turing Thesis (or Cobham's thesis) states that any 'reasonable' model of computation can be equivalent to Turing Machine model in at most polynomial time overhead. People ...
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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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Question regarding notation of a language decidability

$1.\: A_{DFA} = \{\langle B, w \rangle \mid B \text{ is a } DFA \text{ that accepts input string } w \}$ $2.\:A_{DFA} = \{\langle B \rangle \mid B \text{ is a } DFA \text{ that accepts input string } ...
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Church-Turing Thesis - the mechanical model - the turing machine- its limits and its equivalence with a modern digital computer

Well in many texts and places I have seen a called statement, which claims it self to the famous "Church Turing Thesis". I have seen many texts say that based on Church-Turing Thesis : &...
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Computability of function composition

I have some problems to understand computability and hope you can help me. In the lecture we had following problem: Consider the three partial functions $f,g,h\colon N \to N$, where $f$ is computable ...
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The Church-Turing thesis and Hyper-computation

I am not a computer scientist and this is my first question. This question is a question in layman terms and I also want the answer in layman terms. When I searched hyper-computation. There was a list ...
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154 views

Kleene's Theorem and TMs

I wanted to know that based on Kleene's theorem (a language is regular iff some FSA recognizes it), does every regex have a TM (Turing machine) that halts on exactly the same language? Is this ...
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123 views

Are there more Turing-unrecognizable languages than recognizable?

Say you generated a language by looking at the output of a lexicographic enumerator and flipping a coin for each string, adding it to the language on heads. What would be the chance of this language ...
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Halting problem for turing machines with one input

My question is: Is there a simple construction similar to Turing's 'liar' program that shows that Turing machines plus a halting oracle cannot decide if a given Turing machine halts on all inputs. ...
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Computational power of a Turing Machine with infinite states

Consider a turing machine with infinite states. This machine is identical to a regular machine. Only that number of states could be infinite. Does this machine has more computational power than a ...
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52 views

running RAM on a given input

I understand how RAM commands work but I am unable to understand how we use a given input string and find the output. For instance, there's a Random Access Machine which has an input {0,1}*. The ...
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change turing machine to RAM

How can we convert a given Turing Machine into a Random Access Machine? I understand that we can use the transition function to come up with a sort of algorithm but how can we translate all of it into ...
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176 views

How to prove the language of all Turing Machines that accept an undecidable language is undecidable?

I want to prove that $L=\{\langle M \rangle |L(M)\text{ is undecidable}\}$ is undecidable I am not sure about this. This is my try : Suppose L is decidable. Let $E$ be the decider from $L$. Let $A$ be ...
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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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50 views

Is the languague L={<M>, M accepts a finite amount of words} decdidable?

Is $L=\{<M> | L(M) \ is \ finite\} $ decidable ? M is a TM. I think its relative simple to proof with the theorem of rice. But I am interested in a solution which does not use the Rice theorem. ...
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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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About computable sets

Let TOT be the set of all Turing Machines that halt on all inputs. Find a computable set B of ordered triples such that: TOT = {e : ($\forall$x)($\exists$y)[(e, x, y) $\in$ B] This definition means ...
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616 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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There are functions with f (n) = f (2n) which can't be calculated

I have to proofe that there are functions defined by $f:\mathbb{N} \rightarrow \mathbb{N}, f(n)=f(2n), \forall n\in \mathbb{N}$, which are not-computable. However I'm not really sure about the correct ...
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Why is nondeterminism physically not realizable?

Why it is so hard to make a nondeterministic computer? If such a device is physically realizable then would that be a counterexample to the extended Church-Turing thesis?
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Are Turing unrecognizable and undecidable languages, recognized and decided by hyper computation?

Do the hyper computing machines/models that are supposed to be more powerful than Turing machines, capable of recognizing and deciding the languages that are not recognizable/decidable by Turing ...
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109 views

Some questions about the Computability of Turing Machines

I'm learning for a test and I have some important questions about Computability of deterministic and non deterministic Turing Machines. Consider we have the partial functions $f,g,h,t: \mathbb{N} \...
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Can current quantum computers decide languages that Turing Machines cannot?

I am currently learning Computing Theory at university, and we were on the topic of Turing-Decidability, Recognizability, etc. Showing that a problem is undecidable with Turing machines due to ...
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Universal Turing Machine run on Universal Turing Machine

I am curious, what happens if we run Universal Turing Machine on itself?
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134 views

Turing machine where the next step is determined by the state and the symbols up to the read/write head

Given a modified type of turning machine where $\delta = Q\times \Gamma^* \implies Q\times \Gamma \times \{L,R\}$ where the next step of the machine is determined by the current state and whatever ...
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165 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
661 views

How to come up with a language that is recognizable but not co-recognizable?

Forming a language that is recognizable but not co-recognizable. I'm having trouble coming up with a language with these properties. A recognizable language is a language $A \subseteq \Sigma^*$ iff $A ...
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Does this article imply that Turing-Computability is not the same as "effectively computable"?

I've stumbled across this article. It says that there is a problem that only Quantum Computers can solve. In my understanding, this should mean, intuitively, that this problem is "effectively ...
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238 views

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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80 views

Empirical evidence for the Church-Turing thesis in other disciplines

I am aware of the fact that, since the concept of "effectively calculable function" is not rigorous or formally definable, the Church-Turing thesis may not be proven by symbolic or formal reasoning ...
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Would any continuous model of the universe have/be based on hypercomputational laws?

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that: "The universe ...
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120 views

Church-Turing thesis and hypercomputation?

The Church-Turing is a hypothesis about the nature of computable functions. It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource ...
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1answer
116 views

The Church-Turing Thesis (Hello World tester) contradiction and randomized algorithms

The Church-Turing thesis proves that there is no algorithm (or program) $H$ that says whether a program $P$ written in a language, say $C$, on an input $I$ outputs the sentence ...
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3answers
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Is a Turing machine too strong of a model to model physical computation?

I've heard many times people debate the possibility of a real world computation that is impossible for a Turing machine, especially in the context of a human mind. Implying that the Church-Turing ...
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Isn't the given characterisation of recursively enumerable subsets of the class of all recursively enumerable languages?

$S$ is a subset of the class of all recursively enumerable languages over some finite symbols then $S$ is recursively enumerable iff If $L$ is in $S$ and $L'$ is a language such that $L ⊆ L'$ and $L'$...
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Do any programming languages use general recursive functions as their basis?

This is a naïve and, therefore, possibly malformed question, so apologies in advance! My view is that a Turing Machine can be seen as the computational basis for procedural/imperative programming ...
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Comparing turing based programming languages

According to Turing thesis, Can we say all programming languages that support turing machine like C have same power for solving problems and performing algorithms? In other words is there any ...
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The evolution of the term "recursive" from Goedel to Church to present day

I'm currently studying some of the history of computation / computability, in the early days known as recursion theory. I see Goedel's definition of recursive functions seems significant in his paper,...
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The rules for Turing Machine ,equivalence?

We have regular expression for DFA and NFA, at the same time, we have CFG for PDAs, What do we have for Turing Machine? If this questions is too obvious, please points me some reading, I am just ...
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Turing machine + time dilation = solve the halting problem?

There are relativistic spacetimes (e.g. M-H spacetimes; see Hogarth 1994) where a worldline of infinite duration can be contained in the past of a finite observer. This means that a normal observer ...
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679 views

prove A is co-re

Working on some cs theory and solving a problem on computationally [=recursively] enumerable languages: A language $A\subseteq \{0,1\}^*$ is co-c.e. if and only if there is a decidable language ...
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112 views

It is possible to write any program (i.e. Turing complete) with just one single expression?

So I'm currently taking discrete math II at my university and I came across a somewhat philosophical question (so I apologize if this is question is hard to answer precisely) of whether mathematicians ...
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Church-Turing Thesis and computational power of neural networks

The Church-Turing thesis states that everything that can physically be computed, can be computed on a Turing Machine. The paper "Analog computation via neural networks" (Siegelmannn and Sontag, ...
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The Church-Turing-Thesis in proofs

Currently I'm trying to understand a proof of the statement: "A language is semi-decidable if and only if some enumerator enumerates it." that we did in my lecture. One direction of the proof goes ...
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weak Church-Turing thesis

(weak) Church-Turing thesis states every physically realizable computation device can be simulated by a Turing machine (not necessarily efficiently). (1) Then Does any model that is not physically ...
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Does computability according to Church-Turing thesis include side effects?

To my understanding: The Church-Turing thesis means that one could theoretically compute anything that can be computed using either a Turing Machine or the Lambda Calculus. The Lambda Calculus is ...
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Is a physical process with unbounded input Turing equivalent?

Church-Turing thesis states that any effectively computable process is computable by a TM. Let's assume for now that it means that every physical machine is computable by a TM. Let's call it A. Now ...