# Questions tagged [turing-machines]

Questions about Turing machines, a theoretical model of mechanical computation capable of simulating any computer program.

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### Is non-determinism in a non-deterministic turing machine different from that of finite automata and push down automata?

Let a input string be given as $w_1w_2...w_n$. Then if a NFA is currently in state $r$ ( and has read the input upto alphabet $w_i$ ) then before reading the next input symbol the NFA splits into two ...
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### How is it valid to use oracles in mathematical arguments?

Oracles do not exist. If one did exist, then you would replace them with a subroutine with computational requirements and you would no longer need an "Oracle". Thus, Oracles do not exist almost by ...
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### Why is the halting problem decidable for LBA?

I have read in Wikipedia and some other texts that The halting problem is [...] decidable for linear bounded automata (LBAs) [and] deterministic machines with finite memory. But earlier it is ...
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### Do Turing machines assume something infinite at some point?

In a previous question What exactly is an algorithm?, I asked whether having an "algorithm" that returns the value of a function based on an array of precomputed values was an algorithm. One of the ...
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### How do nondeterministic Turing machines compute general function problems?

(Hope this hasn't been asked before, but I didn't find anything.) In my understanding, nondeterminism applies to decision problems only, due to the requirement of the existence of an accepting path. ...
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### Program synthesis, decidability and the halting problem

I was reading an answer to a recent question, and sort of a strange, ephemeral thought came to mind. My asking this might betray either that my theory chops are seriously lacking (mostly true) or that ...
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### Two-State Turing Machine for Parenthesis Matching

In college we have been learning about theory of computation in general and Turing machines more specifically. One of the great theoretical results is that at the cost of a potentially large alphabet (...
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### Why is the halting problem semi-decidable?

This is what is know about halting problem and semi-decidability :- Halting problem says that for a given input x and a machine H, we can't say whether the machine H halts or not on input x. A ...
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### Is the language of TMs that decide some language Turing-recognizable?

Is the language $\qquad L=\{ \langle \text{M} \rangle \; | \; \text{M is a Turing machine that decides some language} \}$ a Turing-recognizable language? I think it's not, as, even if I am able ...
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### Can a Turing machine have infinite states?

Does it make sense for a Turing machine to have infinite number of states ? I had previously asked a question Can Turing machines have infinite length input. From which I came to know about Type-2 ...
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### Proving decidability of language

Prove or disprove: The following language $L$ is decidable: $\{ \langle M, t\rangle: M \text{ is a Turing machine and } \forall w \in \{0,1\}^* [M(w) \text{ halts in at most } t \text{ steps} ]\}$ ...
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### Difference between Turing machine and Universal Turing machine

I've read what's a Turing machine and an UTM are, but I don't get the difference. What does an UTM can do which a normal Turing machine can not?
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### Given a Turing machine , How to construct a efficient boolean circuit?

The proof of $P\subseteq P_{\\poly}$, Let $M$ is a Turing machine with $T(n)$ is running time and goal here is to design a boolean circuit of size $O(T(n))$ (for more detail see Arora and Barak page ...
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### Is the halting problem specific to Turing machines?

The proofs that the halting problem is undecidable seem to make very few assumptions about the kind of program/machine under consideration: just that the programs take one input and either loop or ...
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### Is it decidable whether a Turing machine modifies the tape, on a particular input?

Is $L=\{\langle M,w \rangle|M\text{ does not modify the tape on input w}\}$ decidable? We could tell if a TM does not modify the tape on any input by checking if there are no transitions in $M$ that ...
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### Why does NTIME consider the length of the longest computation?

In Sipser's textbook "Introduction to the Theory of Computation, Second Edition," he defines nondeterministic time complexity as follows: Let $N$ be a nondeterministic Turing machine that is a ...
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### Can we read N numbers in O(N) time?

In a different post it came up that (using the Turing machine model of computation), it is not even safe to say that $N$ numbers can be read in $O(N)$ time. To me this is boggling since it's ...
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### Multitape Turing machines against single tape Turing machines

Introduction: I recently learned that a multi-tape Turing Machine $\text{TM}_k$ is no more "powerful" than a single tape Turing machine $\text{TM}$. The proof that $\text{TM}_k \equiv \text{TM}$ is ...
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### Why is it that every k-tape Turing machine has a 1-tape TM that runs in $O(t^2(n))$?

Apparently, for every k-tape Turing machine that runs in time $O(t(n))$, there exists a 1-tape Turing machine that runs in $O(t^2(n))$. I can see how any multi-tape machine $M$ can be simulated by a ...
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### Can I construct a Turing machine that accepts only its own encoding?

Is the set $S$ = $\lbrace M \mid M \text{ is a Turing machine and }L(M)=\lbrace \langle M\rangle\rbrace\rbrace$ empty? In other words is there a Turing machine $M$ that only accepts its own encoding? ...
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### $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular

Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side. I need to Show that $L$ is regular. I'd relly like some help, I tried to think of any way to prove it but I didn't ...
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### What does $A^B$ mean?

What does $A^B$ mean where A and B are complexity classes? The "Polynomial Hierarchy" page says: $A^B$ is the set of decision problems solvable by a Turing machine in class A augmented by an oracle ...
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### Undecidable unary languages (also known as Tally languages)

An exercise that was in a past session is the following: Prove that there exists an undecidable subset of $\{1\}^*$ This exercise looks very strange to me, because I think that all subsets are ...
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### Given a Turing Machine M, are there infinitely many Turing machines that recognize L(M)?

I want to show this problem is decidable by describing a TM that answers the question. I originally thought this was quite simple, and that the answer would just be a TM that outputs "yes" for any ...
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### Timely lower bounded Turing machines

Let M be a deterministic Turing machine wich has the properties: 1) $\forall x,y \in \Sigma^* : t_M(xy) \ge t_M(x) + t_M(y)$ 2) $\forall a \in \Sigma: t_M(a) \ge 1$ (Also 2) should be obvious for ...
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### A Turing Machine that Doesn't Move to the left [duplicate]

My question is if the following statement is true or false: Does every turing-recognized $B$ language has a turing machine $M$ that recognizes $B$ and fullfiles the following statement: For ...
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### Turing machine that increments a binary number by 1

I was asked to construct a Turning Machine that computes the increment of a binary string by 1- The Turing Machine receives a binary string and accept a string which is an increment by 1 of the input, ...
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### P=NP, isn't it?

Cook and Levin showed in 1971 how deterministically in polynomial time from every non deterministic Turing machine M, that halts in polynomial number of moves/steps, and string w to create the boolean ...
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### Prove that $H$ reduces to $H\varepsilon$

I have to prove that $H_\varepsilon = \{<M> \mid M\ \text{halts on input }\varepsilon\}$ reduces to $H$ (the halting problem). I am very confused how to PROVE it, I mean it is clear that we can ...
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### Show that the collection of Turing-recognizable languages is closed under homomorphism [duplicate]

I have seen this question here, Closure of Turing-recognizable languages under homomorphism But actually this question answers the question of "What is the relation between homomorphism and ...
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### A second question on “Show a TM-recognizable language of TMs can be expressed by TM-description language of equivalent TMs” [duplicate]

Let B={M1,M2,...} be a Turing-recognizable language consisting of TM descriptions. Show that there is a decidable language C consisting of TM descriptions s.t. every machine in B has an equivalent ...
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### Turing machine deciding $\{1^{2^n} : n \geq 0 \}$ [duplicate]

How can I design a Turing machine that accepts the language $\{1^{2^n} : n \geq 0\}$? Here is my attempt: [![enter image description here][1]][1]
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### Prove Undecidability: TM M enters each of its states on Input W?

Consider the following problem: given a Turing Machine $M$ and an input string $w$, does $M$ enter each of its states during its computation on input $w$? How to prove that the problem is undecidable?...
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### How can a Turing machine write the description of the n-th Turing machine?

I am trying to interpret the following problem: "Describe an algorithm for a Turing machine which receives the integer n as input and proceeds to write the description of the n-th Turing machine from ...
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### Undecidable among these for turing machine

Below are two questions I found in Theory of Computation book but couldn't find its correct answers, can anyone please give correct answers with explanation? It is undecidable, whether an arbitrary ...
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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 ...