Questions tagged [turing-machines]

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

Filter by
Sorted by
Tagged with
-2
votes
0answers
64 views

Does busy beaver function of Riemann hypothesis imply it can be proved in a finite time? [closed]

I am not computer science background, just came across a paper https://www.scottaaronson.com/busybeaver.pdf We present a 5,372-state Turing machine that encodes Riemann’s hypothesis; in other words, ...
3
votes
0answers
95 views

Detailed proof of Theorem 2.1 in Papadimitrou book (Multitape TM to SingleTape TM)

I want to know if anybody knows a detailed proof of Theorem 2.1 of Papadimitrou's book Computational Complexity. The theorem states "Given any $k$-string Turing machine $M$ operating within time $...
7
votes
1answer
119 views

Q: Trusting program output from an untrusted machine

Let's suppose that we create a program P, that given input I, generates output O. We then want to run this program on an untrusted computer C that may either want to tamper with the program (run P' ...
1
vote
0answers
103 views

Does any physical process constitute a "computation"? [closed]

I am trying to sharpen the convex hull of what seems like a (surprisingly) stubborn concept to enclose based on answers here, as well as conversations with others, around the nature of what actually ...
0
votes
1answer
106 views

Complexity for universal Counter Machine with {0,1}-valued registers

Consider a universal $\{0,1\}$-$k$-counter machine where each of the $k$ registers has a value in $\{0,1\}$ (as opposed to any non-negative integer in the usual formulation), and there are states $q_1,...
5
votes
1answer
290 views

Is coRE closed under concatenation?

I know that RE is closed under union, intersection, and concatenation (but not complement). It is likewise easy to show that coRE is closed under union and intersection (but not complement). What ...
0
votes
0answers
131 views

Is BigInteger-based Brainfuck Turing Complete?

All of the proofs of Turing-Completeness I've found for Brainfuck rely on its cells being fixed-width integers that wrap around upon over/underflow. The "parent language" P'' on which ...
2
votes
0answers
99 views

Halting behavior of a randomly selected Turing machine?

Let $TM(k,2)$ be the set of Turing machines with $k$-states and $2$ symbols. Let $h(k)$ be the number of machines in $TM(k,2)$ that halt when run on the blank input. Is $\lim_{k \to \infty} \frac{h(k)...
7
votes
1answer
232 views

Is there a concept of "Lego complete"? If not, does it make sense to develop one?

We know the concept of Turing Completeness. These days when I play lego with my kids. I realised that Lego is kinda like programming language: we can build a lot of things with a fairly small set of ...
3
votes
1answer
243 views

Formalization of simulation for Turing machines

Right now I am trying to understand the concept of simulation in theoretical computer science, focussing on Universal Turing machines. All textbooks that I looked into only explain examples. They ...
14
votes
1answer
829 views

Are there languages decidable in linear time by RAM machines that have superlinear time complexity lower bounds for Multitape Turing machines?

Question: Are there languages decidable in linear time by RAM machines that have superlinear time complexity lower bounds for Multitape Turing machines? Background: I recently stumbled upon the ...
1
vote
0answers
106 views

Functional abbreviation for Inst expression in Turing's 1936 paper

In Turing's 1936 paper "On Computable Numbers", For a Turing Machine $M$, $Inst(q_i S_j S_k L q_l ) $ means that if $M$ scans symbol $S_j $ under $m-configuration$ $q_i$, then the symbol ...
7
votes
1answer
318 views

How fast is an equivalent 2-tape TM compared to a $O(n^2)$ 1-tape TM?

In $O(n^2)$ steps, a 1-tape TM can simulate a 2-tape TM that runs for $O(n)$ steps. How fast is an equivalent 2-tape TM known to run compared to a $O(n^2)$ time, 1-tape TM? "Open question" ...
3
votes
2answers
232 views

Dependence of decidability on the encoding of Turing machines

Let $f : \{0, 1\}^* \to \{0, 1\}^*$ be a computable function. Given any encoding $\left<M\right>$ of Turing machines over binary (i.e., a function from the set of Turing machines to the set of ...
1
vote
1answer
182 views

How come Wikipedia says that Random Turing Machines can provide uncomputable output?

Wikipedia article mentioned : Hypercomputation The third paragraph starts off with: Technically, the output of a random Turing machine is uncomputable; however, most hypercomputing literature focuses ...
1
vote
1answer
143 views

What kind of computational model is the brain? [duplicate]

I was wondering what kind of computational model is the human brain (as it seems superior to a Turing machine). Another thing that should be a separate question, What would be a perfect computer model ...
0
votes
0answers
111 views

Can you diagnolize without mentioning simulation?

Are there any known diagonalization proofs, of a language not being in some complexity class, which do not explicitly mention simulation? The standard diagnolization argument goes: here is a list of ...
1
vote
0answers
71 views

Given a program specification, S, what can be said about the size and efficiency of programs that exactly satsify S, with respect to the size of S?

Suppose we are given a program specification, $S$, and we want to reason about programs $P$ that satisfy $S$. One might like to think that if the specification is 'simple', the the program should be '...
-3
votes
1answer
56 views

Show that membership in L is undecidable [closed]

Let L ⸦ {0, 1}* be the language {(M, x) | Turing Machine M on input x enters every state of M at least once}. How can I show that membership in L is undecidable?
6
votes
1answer
167 views

Is $L \subset 1NL$ when $L \neq NL$?

A log-space Turing machine has a read-only input tape, a write-only output tape and uses at most $O(\log n)$ space in its read-write work tapes. The classes $L$ and $NL$ contain those languages which ...
3
votes
1answer
129 views

$DTIME_1(o(n^2))\setminus$ REGULAR

Maybe this is well-known, but I couldn't find any example of a non-regular lanugage that is decidable on a single-tape Turing machine in subquadratic time. Help! Related paper: On the structure of ...
2
votes
1answer
262 views

Prime factorisation of decidable problems

Disclaimer: I am not a theoretical computer scientist. The set of decidable problems $\mathbb{D}$ is countable so $\lvert \mathbb{D} \rvert = \lvert \mathbb{N} \rvert$ and this led me to the ...
2
votes
0answers
74 views

Can $\mathsf{P}^{\#\mathsf{P}}$ be described in terms of a non-deterministic (alternating) Turing machine?

Can the $\mathsf{P}^{\#\mathsf{P}}$ (= $\mathsf{P}^{\mathsf{PP}}$) class be described in terms of a non-deterministic Turing machine (in particular, an alternating Turing machine)? And would a $\...
0
votes
2answers
192 views

Is the decidability of a language decidable? [closed]

Is there a Turing machine that takes a language as input and decides/semi-decides if it is a decidable language? Comments + answer say trivially the answer is yes; however, I'm wondering here would ...
1
vote
2answers
474 views

Why NL is not L

I'm a beginner in learning complexity and get confused at NL. NL is the class of languages that are decidable in logarithmic space on a nondeterministic Turing machine. In other words, NL = NSPACE($\...
-1
votes
1answer
179 views

Evidence integer multiplication is in linear time?

After millenia of quest we have identified two $n$ bit integers can be multiplied in $O(n\log n)$ time. Please refer details in https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-...
10
votes
1answer
3k views

Did Alan Turing's student Robin Gandy assert that Charles Babbage had no notion of a universal computing machine?

Robin Gandy was a student of Alan Turing. Gandy did an analysis of Babbage's Analytical Engine (see 'Gandy - The Confluence of Ideas in 1936' quoted in 'Herken, Rolf - The Universal Turing Machine—...
5
votes
0answers
295 views

Does Depth-First-Search admit a quasilinear time algorithm in mutitape Turing Machine model?

Depth-First-Search (DFS) has a quasilinear (i.e.,$\widetilde{O}(m+n)$) time algorithm in random access model (RAM). I am curious about whether DFS still admits a $\widetilde{O}(m+n)$ time algorithm in ...
1
vote
0answers
62 views

Asymptotic time required to simulate a Turing machine M for k steps

Problem: Given an encoding of a Turing machine M and a natural number k as input, find the output of M (given a blank tape) after k steps. Wikipedia's page on EXPTIME-complete says it takes O(k) time ...
7
votes
1answer
314 views

Uniform mortality problem for Turing Machines

Consider the following generalisation of the mortality problem for Turing Machines. Given a Turing Machine $M$. Is there a bound $k_M$ such that starting from any configuration $c$ machine $M$ ...
9
votes
1answer
333 views

Turing Machines as Coalgebras

I'm looking to write a survey on the method of representing the dynamics of state-based computation within the framework of coalgebras. So far I've managed to find papers on coalgebra representations ...
0
votes
1answer
181 views

Why does the Placid Platypus function grow faster than any computable function?

I came across the Placid Platypus function $PP(n)$ today, defined as the minimal number of states needed for a turing machine that prints a string of $n$ ones and halts. This function is claimed to (...
-2
votes
2answers
173 views

Do Turing complete languages automatically have efficient algorithms [closed]

Every Turing complete programming language can describe an algorithm that sorts sequences. Is it also true that every Turing complete language can describe an algorithm that sorts sequences in $\...
5
votes
1answer
186 views

Minimal information needed for determine some function

From calculus, we know that if someone has a continuous function $f$, it is enough to know $f$'s values on the rationals in order to know $f$ on the entire line. In some sense, a "countable amount of ...
1
vote
0answers
177 views

Solving the Halting problem for most inputs [closed]

Is it possible to solve the following version of the Halting problem : given any Turing machine and some input tape, the program should answer if this pair halts or not except possibly for one Turing ...
7
votes
2answers
589 views

Are all turing machines paths predictable?

I was recently studying partial solutions to the halting problem and came across the problem which I discuss below. In particular I was studying when it was computable to tell if a turing machine has ...
1
vote
0answers
42 views

Question About Turing Machine Computability [closed]

If p is a Turing machine then L(p) = {x | p(x) = yes}. Let A = {p | p is a Turing machine and L(p) is a finite set}. Is A computable? Justify your answer. So I'm trying to figure out how to solve ...
4
votes
0answers
83 views

Libraries for programming automata and Turing machines

What are the most useful libraries around for coding related to automata and Turing machines? By useful I mean the number of functions and algorithms supported by it.
5
votes
0answers
390 views

Games on Turing machines that are AH-hard

I'm interested in proving that finding optimal play in a particular two-player game is harder than the arithmetic hierarchy. I suspect this to be true, because even carrying out a deterministic end-...
-1
votes
1answer
511 views

What is the practical importance of making or using a Turing complete language? [closed]

I get what a Turing machine is and what language is a Turing-complete language but when someone introduces me to a new programming language (like Solidity) and says it is Turing complete, what am I ...
2
votes
2answers
512 views

For a specific unbounded Turing machine, is its Halting problem undecidable?

The question is on the title. To make it clearer, I state some facts. We all know that the Halting problem with input is undecidable. It leads to, given a specific input (e.g. empty string), the ...
12
votes
1answer
1k views

How good can a halting detector be?

Is there a Turing Machine that can decide whether almost all other Turing Machines halt? Suppose we have some enumeration $\mathbb{N} \rightarrow \{M_i\}$ of Turing machines, and some notion of "...
1
vote
1answer
313 views

What is the VC dimension of Turing machines with specified maximum size?

Note by "maximum size" in the question I'm referring to the size of the Turing machine's state machine. I chose Turing machines in the question to make the question concrete, but I'm also more ...
5
votes
1answer
183 views

Turing machines over a structure

I have heard of models of computation where you have a Turing machine, but instead of symbols over a finite alphabet you have elements from some tau-structure, and write instructions are replaced with ...
4
votes
2answers
1k views

Enumerating decidable languages

[The assumption in this question is wrong. It is possible to enumerate exactly the decidable languages with semideciders.] Lets say we have a TM $M_E$ enumerator that writes out codes of TM's on a ...
1
vote
2answers
272 views

What is the time complexity of base conversion on a multi-tape Turing machine?

Base conversion is the problem of converting an integer between representations in two fixed bases. Without loss of generality consider the case of relatively prime bases. I think it's easier to ...
28
votes
1answer
1k views

Functions that are Not Efficiently Computable but Learnable

We know that (see, e.g., Theorems 1 and 3 of [1]), roughly speaking, under suitable conditions, functions that can be efficiently computed by Turing machine in polynomial time ("efficiently computable"...
4
votes
0answers
263 views

How fast can we sort a list if we know how it was written?

Let $G$ be a linear time (deterministic) turing machine that takes positive integers $n$ in unary to lists of length $n.$ For any fixed such $G$, define sparse-sort(G,n) as the problem of sorting the ...
-2
votes
1answer
471 views

What's the differences between "A language is computable by a TM" and "A language can be decided by a TM"? [closed]

I am reading two books about the Turing Machine. "Computational Complexity" by Christos H. Papadimitriou. "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak. However, the ...
-2
votes
2answers
246 views

Why bother with deterministic Turing machines when nondeterministic Turing machines consume less space and time? [closed]

I have a question on a part from the wikipedia page on Savitch's theorem: https://en.wikipedia.org/wiki/Savitch%27s_theorem The part in question is the following: [...], if a nondeterministic ...

1
2 3 4 5