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)

Filter by
Sorted by
Tagged with
0
votes
1answer
51 views

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. ...
0
votes
1answer
62 views

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 ...
-2
votes
1answer
43 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 ...
0
votes
1answer
40 views

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 ...
1
vote
1answer
70 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 ...
3
votes
2answers
40 views

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 ...
0
votes
1answer
29 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. ...
0
votes
2answers
20 views

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^...
0
votes
1answer
36 views

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 ...
2
votes
4answers
445 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 ...
0
votes
2answers
49 views

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 ...
-1
votes
2answers
81 views

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?
0
votes
1answer
62 views

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 ...
0
votes
1answer
65 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} \...
3
votes
1answer
91 views

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 ...
0
votes
0answers
91 views

Is “Extended Church-Turing Thesis” the same as “Cobham-Edmonds Thesis”?

I have been looking for any reference regarding the term: "Extended Church-Turing Thesis" [some people will call it, Strong Church–Turing Thesis]? Does anyone defined it or it is just people in ...
1
vote
0answers
52 views

Universal Turing Machine run on Universal Turing Machine

I am curious, what happens if we run Universal Turing Machine on itself?
1
vote
2answers
100 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 ...
0
votes
2answers
70 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?
2
votes
1answer
208 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 ...
8
votes
2answers
1k views

Does this article imply that Turing-Computability is not the same as “effectively computable”?

First of all, I apologize if this has been asked, but I truly didn't find anything. I've stumbled across this article. It says that there is a problem that only Quantum Computers can solve. In my ...
1
vote
1answer
82 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 ...
1
vote
1answer
76 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 ...
1
vote
2answers
84 views

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 ...
0
votes
0answers
75 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 ...
0
votes
1answer
48 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 ...
2
votes
3answers
248 views

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 ...
0
votes
1answer
59 views

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 $L'$...
23
votes
2answers
7k views

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 ...
0
votes
1answer
37 views

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 ...
5
votes
0answers
51 views

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,...
1
vote
0answers
30 views

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 ...
15
votes
5answers
4k views

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 ...
1
vote
2answers
406 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 ...
1
vote
1answer
111 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 ...
30
votes
2answers
4k views

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, ...
3
votes
1answer
303 views

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 ...
2
votes
1answer
150 views

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 ...
6
votes
3answers
239 views

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 ...
0
votes
2answers
61 views

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 ...
12
votes
3answers
2k views

Can every self-modifying algorithm be modelled by a non-selfmodifying algorithm?

If we have any arbitrary computer program that can modify its instructions, is it possible to simulate that program with a program that cannot modify its instructions? Edit: I am new to ...
1
vote
0answers
58 views

Canonical definition of suitable encoding

I've had several Computer Science courses and, from what I recall, I've never been given a rigorous definition of suitable encoding. Definitions always tend to use effective method or some synonym to ...
8
votes
1answer
176 views

Church-Turing and physical PDEs

When I read about the Church-Turing thesis it seems to be a common claim that "physical reality is Turing-computable." What is the basis for this claim? Are there any theoretical results along these ...
3
votes
1answer
129 views

Whatever that can be done using algorithm can be done using Turing machine

In 1937 how was Alan Turing so sure that all that can be done using algorithms can be implemented using a Turing machine? Since that period many new algorithms were implemented. What was his ...
0
votes
0answers
126 views

Does Turing Completeness imply the existence of a Universal Program?

Please correct me if at any time my definitions are wrong. Suppose we have a programming language $L$ over some set $D$ with semantic (partial) n-ary functions $\varphi^n:D \to (D^n \to D)$. Assume $L ...
6
votes
3answers
940 views

Would creating a complete computer simulation of the human brain prove the Church-Turing thesis?

According to Wikipedia, the Church-Turing thesis "states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing ...
2
votes
4answers
265 views

Problems understanding proof of smn theorem using Church-Turing thesis

I am reading Barry Cooper's Computability Theory and he states the following as the s-m-n theorem: Let $f:\mathbb{N}^2\mapsto\mathbb{N}$ be a (partial) recursive function. Then there exists a ...
17
votes
3answers
8k views

Is there any uncountable Turing decidable language?

There are many(and I mean many) countable languages which are Turing-decidable. Can any uncountable language be Turing decidable?
5
votes
0answers
203 views

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 ...
4
votes
3answers
559 views

Can every program be parallelized infinitely and automatically?

In my previous question ( Can Turing machines be converted into equivalent Lambda Calculus expressions with a systematic approach? ), I got the answer that it is indeed possible. And as I have read ...