The Turing machine is a fundamental model of computation, especially in theoretical work.

learn more… | top users | synonyms

-2
votes
0answers
37 views

What does $\Gamma^*$ mean in “THE P VERSUS NP PROBLEM”? [on hold]

I am recently reading the document "THE P VERSUS NP PROBLEM" written by STEPHEN COOK. I downloaded the document from the url http://www.claymath.org/sites/default/files/pvsnp.pdf. On page 10, there is ...
30
votes
9answers
12k views

Real computers have only a finite number of states, so what is the relevance of Turing machines to real computers?

Real computers have limited memory and only a finite number of states. So they are essentially finite automata. Why do theoretical computer scientists use the Turing machines (and other equivalent ...
4
votes
1answer
36 views

What is the simplest universal unidimensional interaction net system?

The Interaction Combinators are possibly the simplest multidimensional system of interaction nets that is Turing-complete. What about interaction nets with only 2 ports - 1 principal, 1 auxiliary? ...
1
vote
0answers
69 views

Langton's ant questions

I'm a mathematician currently working on the Langton's ant conjecture, just for fun. I have some result but I don't know if they are meaningless. So that is why I'm asking. 1) Is there a mathematical ...
1
vote
1answer
83 views

Multi Head universal Turing machine

It is common knowledge that a universal Turing machine can simulate any Turing machine with logarithmic overhead. Is it possible to make this overhead constant by constructing an analogous "Universal" ...
10
votes
1answer
116 views

Do bounded-visit nondeterministic linear bounded automata recognize only regular languages?

Do bounded-visit nondeterministic linear bounded automata recognize only regular languages? By a nondeterministic linear bounded automaton (nLBA) I mean a single-tape nondeterministic Turing machine ...
4
votes
1answer
136 views

Does Wikipedia assume a solution to the halting problem in their description of universal one way functions?

(As for the question in the title: the answer must be no, but then I don't understand what is intended.) The Wikipedia page on one way functions states: Goldreich gives one construction of a ...
0
votes
2answers
122 views

Are there any open problems concerning decidability? [duplicate]

I am learning computability theory. I am just interested to know some famous problems (Formally languages) whose decidability is in question.
0
votes
0answers
66 views

How Turing machines compare with process calculi w.r.t. expressivity? [duplicate]

Some time ago there were heated debates, and some researches argued, that so-called interactive computations (understood as "computations=calculations+communication"), like Pi-calculus, actors model, ...
1
vote
0answers
34 views

Maximum entropy definition of universal distribution

Kolmogorov complexity and the "universal distribution" $m$, defined e.g. here and discussed in detail in the book of Li and Vitanyi, are defined with respect to a universal Turing machine (UTM). ...
15
votes
2answers
336 views

Is there a non-deterministic linear time algorithm for CNF-SAT?

The decision problem CNF-SAT can be described as follows: Input: A boolean formula $\phi$ in conjunctive normal form. Question: Does there exist a variable assignment that satisfies $\phi$? I'm ...
-1
votes
3answers
301 views

Fastest Turing Machine

Recently I have been reading about Kolmogorov Complexity. As such I started thinking about the "fastest turing machine". In particular I am not interested in finding such a machine, I am only ...
7
votes
3answers
238 views

Is there a theory of computation that takes failure and decay of the computation substrate into account?

There are obvious differences between a Turing machine and a real computer. Not only is the latter finite in size, it is also prone to failures and it is made from decaying matter. The kind of ...
0
votes
1answer
127 views

Computing the DAG of a program given source code or AST

I've seen many papers on scheduling components or tasks once a DAG for the program is known, either by user-input or by domain restriction (i.e. all cross shaped 5-pt stencil codes have a known DAG). ...
4
votes
0answers
187 views

What would a PDA be with a queue instead of a stack?

A while ago it occurred to me that the stack data model in a push-down automaton could be exchanged for a queue or deque model. I've explored this a bit as a pet project and it looks like an automaton ...
2
votes
0answers
87 views

Space time lower bound with $\mathsf{PSPACE}$ oracle

Does a single tape Turing machine with access to $\mathsf{PSPACE}$ oracle needs more than $\mathsf O(1)$ working tape memory and $\mathsf O(1)$ working time to solve $\mathsf{NP}$-complete problem? ...
1
vote
0answers
46 views

Analogues of different complexity classes in various models

We suspect following relation: $$TC^0\subsetneq NC^1\subsetneq L\subsetneq NL\subsetneq AC^1\subsetneq NC^2\subsetneq P\subsetneq NP\subsetneq PH\subsetneq PSPACE$$ in Turing/boolean circuit ...
1
vote
1answer
134 views

Is Redis Turing Complete?

Is Redis with all its data types (Strings, Lists, Hashes, Sets, Sorted Sets, etc.) Turing Complete?
1
vote
1answer
55 views

Is multiprocessing possible on a Turing Machine? [closed]

I recently created a parallel implementation of the Merge Sort, in which the sorting of several groups was accomplished by different processes, and was wondering if this was theoretically possible on ...
4
votes
0answers
93 views

What is the Kolmogorov complexity of arithmetic?

Chaitin's incompleteness theorem says no sufficiently strong theory of arithmetic can prove $K(n) > L$ where $K(n)$ is the Kolmogorov complexity of the number $n$ and $L$ is a sufficiently large ...
7
votes
0answers
116 views

What can you do with a moving knife besides cutting a cake?

In the fair cake-cutting, two different computational models are used: A discrete model, in which the algorithm issues queries to the players and proceeds according to their replies; A continuous ...
18
votes
2answers
960 views

What functions can System F not compute?

In this wikipedia article on Turing Completeness it states that: The untyped lambda calculus is Turing complete, but many typed lambda calculi, including System F, are not. The value of typed ...
7
votes
1answer
265 views

Was bombe machine turing complete?

In the recent movie called The Imitation Game, there is a affirmation that Turing was building his theoretical machine. That machine is the Bombe Machine. Is this machine really equivalent to a Turing ...
2
votes
1answer
100 views

Simple example of halting-unprovable Turing machine

Is there a simple example of a Turing machine $M$, such that whether $M$ halts or not on the empty input cannot be proved within the current mathematical system? Specifically, I'm curious whether ...
3
votes
0answers
55 views

Is there an easy way to improve this Tree Normal Form for Busy Beaver candidates?

In "Attacking the busy beaver 5" by Heiner Marxen and Jürgen Buntrock, an algorithm to create tree normal candidates is explained (it also contains a concise introduction of the relevant terms). If ...
3
votes
1answer
122 views

What are different definitions of Universal Turing-machine?

I am not sure what is the appropriate way for this, but I would like to collect different possible definitions/variants of Universal Turing-machines. Here are the ones I know, post below if you know ...
9
votes
2answers
409 views

Looking for Literature Source for Following idea

I am quite certain that I am not the first to entertain the idea that I am going to present. However, it would be helpful if I can find any literature related to the idea. The idea is to construct a ...
4
votes
1answer
92 views

Busy beaver candidate elimination: Minimum space requirements

I'm currently enrolled in a course that introduces Turing machines. As I wanted to play around a bit, I wrote a little TM engine and had it search for busy beavers (it successfully found the 4-state ...
0
votes
1answer
131 views

Where is the proof of universality of Rule110 in Stephen Wolfram's book?

I have Stephen Wolfram's book A New Kind Of Science. And I want to find the proof of the universality of Rule 110. I couldn't find the clue in the contents page since it only shows 12 chapters and no ...
0
votes
1answer
78 views

Conflicting definitions regarding TM and Recursively Enumerable languages

In Lewis's and Papadimitriou's book "Elements of the Theory of Computation" the transition table is a function $\delta: Q \setminus F \times \Gamma \rightarrow Q \times (\Gamma \cup \{L,R\})$. ...
3
votes
2answers
233 views

Source of Turing-machine illustration

I am writing a computer science textbook and want to use an illustration showing a Turing machine. Images are all over web, but almost always without authorship/illustratorship credited. I need to ...
1
vote
1answer
183 views

Does hyper-computational power of infinite time Turing machines also require infinite memory?

Can a infinite time Turing machine perform hyper-computation like checking the consistency of the set theory ZF without using infinite memory?
8
votes
2answers
1k views

A total language that only a Turing complete language can interpret

Any language which is not Turing complete can not write an interpreter for it self. I have no clue where I read that but I have seen it used a number of times. It seems like this gives rise to a kind ...
2
votes
0answers
64 views

Relation between the running time of Turing machines with different symbol sets

In Arora and Barak's Computational Complexity, Claim 1.5 says that if a function $f$ is computable in time $T(n)$ by a Turing machine with alphabet $\Gamma$ then it is computable in at most time ...
22
votes
3answers
3k views

P and NP classes explanation through lambda-calculus

In the introduction and explanation P and NP complexity classes often given through Turing machine. One of the model of computation is the lambda-calculus. I understand, that all of models of ...
-1
votes
2answers
95 views

Looking for menu-driven coding editor based on a programming language state machine [closed]

I'd like to know whether an application development environment exists that uses a menu-driven coding editor that employs a programming language state machine. This would mean that commands, variable ...
9
votes
1answer
311 views

Are there non-constructive proofs of existence of “small” Turing machines / NFAs?

After reading a related question, about non-constructive existence proofs of algorithms, I was wondering if there are methods of showing existence of "small" (say, state-wise) computation machines ...
8
votes
2answers
791 views

Turing machines whose termination is unprovable?

I have a naive question: does there exist a Turing machine whose termination is true but unprovable by any natural, consistent and finitely axiomatizable theory? I ask for a mere existence proof ...
2
votes
1answer
242 views

Is it worthwhile to try to prove a conjecture by mapping it to a Turing machine?

Lets assume the proof of a conjecture, for example, the famous Goldbach conjecture. Is it possible to try to prove or disprove such a conjecture by devising a Turing machine that accepts if the proof ...
3
votes
2answers
2k views

Difference between infinite state machines and turing machines

Finite state machines (FSM) are strictly less powerful than turing machines (TM). But this is not the case with infinite state machines (ISM). For example, every TM can be embedded into some ISM. ...
0
votes
1answer
136 views

Simulation of deterministic turing machines

What are the best known upper and lower bounds for simulating t steps of certain models of deterministic turing machines (1 tape, 1 tape with read only input tape, 2 tape, multi tape, with/without ...
4
votes
2answers
285 views

Simulation of every physical quantum system on quantum computer

Let me quote from the section 9.3 of Classical and Quantum Computation by Kitaev, Shen and Vyalyi. With high confidence, we may claim that every physical quantum system can be efficiently ...
3
votes
1answer
105 views

Program transformation using partial functions which preserve partial correctness

Much work has been done demonstrating that certain program transformations preserve particular properties. That is, for any program $P$ which has property $\alpha$, show that $P$ transformed under ...
5
votes
0answers
188 views

Regular languages in lambda calculus

With Turing machines, by imposing certain restrictions on the form of the transition function, one can get a machine that accepts only regular languages. I am wondering what is the counterpart in ...
0
votes
0answers
171 views

How to picture Non-Deterministic Turing machine seeking out boolean expression to satisfy examples

Traditionally, the boolean satisfiability problem is framed as, given a boolean formula, is there an assignment that satisfies the formula. I'm trying to look at this differently - from the ...
13
votes
1answer
1k views

Computing input length on a one-tape Turing machine

In connection with this question it occurred to me to wonder: what is the time complexity for a single-tape single-head Turing machine to compute the length of its input? To be specific, let's say ...
0
votes
1answer
83 views

Is refuting candidate deciders of the halting problem computable? [closed]

No Turing machine can decide whether any given Turing machine will halt for a given input. That is: If you give me a Turing machine which you claim can take a Turing machine and an input for that ...
7
votes
4answers
475 views

Is there a generalization of the GO game that is known to be Turing complete?

Is there a generalization of the GO game that is known to be Turing complete? If no, do you have some suggestions about reasonable (generalization) rules that can be used to try to prove that it is ...
2
votes
0answers
142 views

Learning about Nested Stack Automata

I want to learn about nested stack automata. However my efforts to find a suitable learning resource have so far been abortive: The Wikipedia article on nested stack automata is a stub. Alfred Aho's ...
10
votes
6answers
2k views

A small C-like language that turing machines can simulate

I am looking for a small language that helps 'convince' students that turing machines are a sufficiently general computing model. That is, a language that looks like the languages they are used to, ...