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Questions tagged [rice-theorem]

Rice's Theorem states that any (non-trivial) property of Turing machines is undecidable.

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Deciding whether a Turing machine decides a language $L$ in at most $n^2$ steps

Let $L$ be a language for which there exists some turing machine deciding it in at most $n^2$ steps. Is it decidable whether a given turing machine $M$ decides $L$ and runs in at most $n^2$ steps? I ...
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How do you use Rice's theorem and why does it make sense? (Use provided Rice's theorem)

So this is the Rice's theorem we were provided: Definition: $TM$-$FUNC(S)$ Input: Turing machine $M$ Question: Is $f_M \in S$ Let $S$ be a set of computable partial functions with $\emptyset \neq S \...
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Exploiting weaknesses in virus-detecting software?

If a virus is defined as a self-reproducing program, then Rice's theorem implies there can be no infallible virus-detecting algorithm. Can we take that one step further, as follows? If you have the ...
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Mapping Reduction from INFINITE to REG

given the following languages: $INFINITE_{T M}=\{\langle M\rangle: M$ is a TM with $|L(M)|=\infty\}$. $R E G_{T M}=\{\langle M\rangle: M$ is a TM with $L(M) \in \mathrm{REG}\}$. prove the following ...
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The language of all machines that accepts strings of even length

I have difficulties in proving that for the given language: $E V E N_{T M}=\{\langle M\rangle: M$ is a TM s.t. $|w|$ is even for all $w \in L(M)\}$. prove that: $E V E N_{T M} \in coRE$ I've tried to ...
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Decidability of the minimum number of states a Turing Machine needs to accept a language

I'm reading some old notes from a course on Turing Machines and I've bumped into the following question: Is the following language decidable? The language formed by the set of all Turing Machines ...
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Turing-reducibility for guaranteed decider

The following exercise is taken from Theoretical Computer Science by Atiba. Use Rice's theorem to demonstrate that every decidable language is Turing reducible to some language that is already ...
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Reductions but no algorithms

in "Introduction to Automata Theory, Languages and Computations" by Motwani, Ullman and Hopcroft, when they need to prove, for instance, Rice's theorem, they reduce the universal language, $...
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Showing that a property is semantic - Rice's theorem

I want to show that the language $$L= \left\{ \left\langle M\right\rangle \mid\substack{\text{M is a TM and there exists a poly TM $M'$ such that}\\ \text{if M halts on input $w$, $M'$ halts on $w$ ...
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Does description method matter in Rice’s theorem?

If $\mathcal{p}$ is a nontrivial property of formal languages, then $L_{\mathcal{p}} = \{ \langle M \rangle \mid L(M) \in \mathcal{p} \}$ is undecidable by Rice’s theorem. What if we describe ...
Omid Yaghoubi's user avatar
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We cannot recognize a set of languages as the language themselves

"We cannot recognize a set of languages as the language themselves" What is the meaning of the line and why we cannot do it and how is the encoding of TM is helping in that?
Sameer Raj's user avatar
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Why is a Language L(M) {has at least 10 strings} turing recognizable and L(N) {has at most 10 strings} is not?

Why is a Language L(M) {has at least 10 strings} recognizable and L(N) {has at most 10 strings} is not? ...
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Undecidability of a set of Turing Machines

Considering the following set, I have to say if it is undecidable, decidable or semidecidable: $$S_1 = \{y | \forall n \text{ the Turing Machine } M_y \text{ does not accept any string of length } n\}$...
Filippo Scaramuzza's user avatar
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Is there a way to tell if ANY machine on ANY input will halt in fewer than n steps OTHER than running the machine for n steps?

Is there a way to tell if ANY machine on ANY input will halt in fewer than n steps OTHER than running the machine for n steps? I've read the similar questions and answers such as here, but I wanted to ...
Garrick White's user avatar
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Rice theorem could apply except RE language?

You know that Rice theorem is applicable to check decidability of RE language. Also we know that all regular, deterministic context free, context free, recursive languages are RE languages. $Q_1:$ So ...
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Could I apply Rice theorem for both TM's property and language property?

I read that Rice theorem applicable only for language property not for machine property. But today I have read from stack exchange and one site they are applying Rice theorem on machine also. My ...
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Prove that "If $L$ is a context-free language, is $\overline{L}$ also context-free?" is undecidable

Lately I need to find the decidability of the following decision problem: If $L$ is a context-free language, is $\overline{L}$ also context-free? I know that context-free language is not closed ...
Abhishek Ghosh's user avatar
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Is this language in RE?

Given the following language: $$L=\left \{ <M> | \exists L \in R \quad s.t \quad L(M)\subseteq L \right \}$$ I need to determine it's compuation class(R or RE). I used Rice Theorem as follows to ...
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Can a TM decide the binary PCP-Problem?

I am having a little bit of a hard time distinguish between a TM which accepts a language, and a $TM$ that decides a language. To be more precise: $L_1 = \{\langle M\rangle\; | \; M$ accepts the 10-...
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A question on decidability

I have a homework question that is as follows: L(P) is a language of ASCII input strings for which a given program, P, returns "yes". Is the set of all input strings P decidable, such that P ...
TheClash's user avatar
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Is my assumption about non trivial propery correct?

"make sure you understand why for a non trivial property $S$, $\bar{S}$ is also non trivial" My assumption is: $S$ is non trivial property: There are L1,L2 such that $L_{1},L_{2}\in RE$ and ...
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Using Rice's theorem to prove undecidability of $E_{TM}$

I saw this proof and I wondered if I could prove $E_{TM}$ with Rice's theorem similar to the one described in the answer. Can you do the same thing by letting $M$ to only accept empty strings? (the $M$...
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Is this a correct application of Rice-Shapiro theorem?

Let $\langle M\rangle$ be the encoding of a Turing machine as a string over $\Sigma=\{0,1\}$, and consider the language $L=\{\langle M\rangle| \text{ $M$ is a Turing machine that accepts a string of ...
sprajagopal's user avatar
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Is there a connection between the Undecidability Theorem and "software complexity"?

I was reading Complexity: The Emerging Science at the Edge of Order and Chaos and a certain passage got me really intrigued. When discussing Chris Langton's explorations of artificial life algorithms,...
Vinicius Andrade's user avatar
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Halting (on empty input tape) for an infinite subset of all Turing machines

As is well known, there is no single procedure for deciding whether any given Turing machine halts on an empty input tape. This is easily shown, e. g., by applying Rice's theorem. But what if, instead ...
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Determine if a language is Decidable or semi decidable

Consider the language $L = \{\langle M \rangle: \text{ $M$ accepts at most two single-letter words}\}$, where $\langle M\rangle$ is the encoding of Turing machine $M$. We need to determine, without ...
Ronit sharma's user avatar
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Is Rice's Theorem equivalent to the Halting problem?

As I understand it Rice's Theorem seems to imply the existence of the Halting problem. That is, with Rice's Theorem, we can prove that the Halting problem is undecidable. However, to me, it seems like ...
user127454's user avatar
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Why is the following language undecidable?

I'm currently learning for my exams this semester and tried to solve some old exams from the last years. The question is to show, that L ist undecidable. $L=\{w|T(M_w)\neq\emptyset \land \forall x \in ...
Florian Bauer's user avatar
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Rice's Theorem for Turing machine with fixed output

So I was supposed to prove with the help of Rice's Theorem whether the language: $L_{5} = \{w \in \{0,1\}^{*}|\forall x \in \{0,1\}^{*}, M_{w}(w) =x\}$ is decidable. First of all: I don't understand, ...
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Prove the language of Turing machines that recognize (01)^* is not recursive

I need to prove $: L=\left\{\langle M\rangle\mid M \text { is a } T M \text { and } L(M)=L\left((01)^{*}\right)\right\} \notin Re$ at first observation it looks like it's immediate from Rice's ...
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All problems about Turing machines that involve only the language that the TM accepts are undecidable

I came across the below statement in the classic text "Introduction to Automata Theory, Languages, and Computation" by Hopcroft, Ullman, Motwani. ...
Abhishek Ghosh's user avatar
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Rice theorem, the proof of the part when the empty language belongs to the property

I was going through the classic text "Introduction to Automata Theory, Languages, and Computation" by Hofcroft, Ullman and Motwani where I came across the proof the Rice theorem as shown. $...
Abhishek Ghosh's user avatar
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EVEN-CFL Decidable / Undecidable - Rice-Theorem

Let EVEN-CFL $=\left\{w | M_{w} \text { is a } \mathrm{TM}, \text { such that } L\left(M_{w} \right) \\ \text{ has only words with even length and is context free.}\right .\}$ Question : Is EVEN-CFL ...
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How can I apply Rice's theorem?

I am learning for my computability and complexity exam in which there is always an exercise to decide whether some problem is decidable or not. In one of the past exams, there was the following ...
Speedding's user avatar
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Why Rice theorem work for decidability?

Rice's theorem states: Every nontrivial property of recursively enumerable language is undecidable. I came across following problems, which Ullman's books say both are undecidable: Turing ...
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Proving that Rice's theorem does not apply to a property

This is related to an assignment, but I would still appreciate help in formalising proof either through private message or on this topic. The question is about if Rice theorem applies to certain ...
Joseph's user avatar
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Decidability of decision problems

Can somebody give intuition how to answer those questions? From one side I can say that most of them are undecidable because we can reduce the halting problem to them (or halting problem can appear ...
Maksym's user avatar
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Rice Theorem - Problem to understand and apply it

I have struggle to understand the Rice Theorem. My understanding of Rice Theorem: The purpose of this Theorem is to proof that some given language L is undecidable iff the language has a non-trivial ...
Schleudergang's user avatar
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1 answer
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How to determine if this problem is decidable?

I am currently stuck on the following problem: Given a WHILE-program P and the knowledge that all input variales are set to 0, is it decidable if a specific instruction is reached 1000 times? My ...
TheMotivatedGeek's user avatar
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Rice's Theorem - usage on $DFA$ or $LBA$

I have read about Rice's Theorem on Sipser's book, and I think I understand it quite well. I understand that it can be used to show that a language is not decidable. However I am not sure about one ...
Alan's user avatar
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Can we enumerate finite sequences which have no halting continuation?

Note: this question has been cross-posted to Math.SE, after about a week here. I am trying to deepen my understanding of the relationship between the Halting Problem and Godel's Completeness Theorem (...
user271667's user avatar
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1 answer
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Rice's theorem applicable to the following language?

Let $L= \{\langle M \rangle \mid M \text{ halts on } \langle M \rangle \} $ be a language where $\langle M \rangle$ is the Code of the TM $M$. $L$ is undecidable. I've heard that I can't use Rice's ...
Marc's user avatar
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Language of TM is Undecidable

why is this Problem$$L = \{ \langle M\rangle \mid L(M) \text{ is undecidable}\}$$ undecidable? I thought if we know $L(M)$ the turingmaschine accepts all $x \in L(M)$, so $L(M)$ is in every case ...
Marc's user avatar
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proof of the rice's theorem

Let $P$ be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given TM’s language has property $P$ is undecidable. Proof:(This is from sipser'...
Khan Saab's user avatar
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3 answers
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What is the Name of the Problem or Technique of Determining if a Line in a Program Will Execute

If I were to pose the question: "Given a program $P$ containing statement $X$, will $X$ be executed (given enough runs with all possible inputs)?" This strikes me of being a relative of the Halting ...
Keenan Diggs's user avatar
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Trying to prove semidecidability of an undecidable language

I have been having a hard time understanding whether the set $S = \{ M \mid |L(M)| = 5 \}$ is semidecidable or not, where $M$ is a generic Turing Machine and $L(M)$ the language accepted by such TM, ...
Antonio Frighetto's user avatar
2 votes
1 answer
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Rice's theorem application on a language that resembles ETM

I'm working on an exercise that involves checking if the Rice's theorem can be applied on a two languages. The first language is $E_{TM} = \{ \langle M \rangle \text{ | M is a Turing Machine and } L(...
Gianguido Sorà's user avatar
1 vote
1 answer
534 views

A question about proving Rice's Theorem by reducing it to the Halting Problem

I've read the definition for Rice's Theorem, here's the one from Wikipedia: In computability theory, Rice's theorem states that all non-trivial, semantic properties of programs are undecidable. ...
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Is L={<M>|M is a TM and L(M) is uncountable} decidable?

Is $L=\{\langle M\rangle\mid \text{$M$ is a Turing machine and $L(M)$ is uncountable}\}$ decidable? My intuition is that it is not, but I'm not sure if Rice's Theorem applies in this case. If it is ...
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1 answer
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How can I build a fool proof security system? [closed]

From what I understand, designing an IT security systems requires to build an algorithm D which can decide whether any program M is malicious or not. That tasks looks very similar to me than deciding ...
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