Questions tagged [rice-theorem]

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

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Can you apply Rice's Theorem on the following languages? Are they decidable?

Can you apply Rice's Theorem on the following languages? Are they decidable? $$L_1:=\{v\mid v \text{ is the Code of a TM } M_v \text{ and } M_v \text{ has an even number of states.}\}$$ $$L_2:=\...
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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 ...
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Use the Rice's theorem to prove that the following property of a Recursive Enumerable language L is undecidable

This exercise was taken from the book "Languages and Machines: An Introduction to the Theory of Computation" by Thomas Sudkamp. It refers to exercise 12 (b) chapter 12. Given a language L which is ...
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Correct Turing machine representation for Rice Theorem proof

Consider the language L1. From Rice Theorem I know L1 is not decidable (i.e. undecidable). L1 = { R(M) | R(M) is a TM and 1011 ∈ L(M)} For example if I want to represent by diagram a TM $M_1$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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How to show that the complement of ATM $\leq_{m}$ L = {<M> : |L(M)| = 2}?

My original intention was to prove that $L = \{\langle M \rangle \mid |L(M)| = 2 \}$ is not turing recognizable but soon I realized that I could use the complement of ATM because the complement of ...
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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 (...
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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 ...
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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 ...
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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'...
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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 ...
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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, ...
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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(...
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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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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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Caroll's paradox => Rice theorem?

To me (but I might be wrong) Rice's theorem asserts that it's not possible to formalise the demonstration of a non-trivial property of a recursively enumerable language within the same given language. ...
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Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem

Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem. Well I did show that with reduction, by using $HP'$. Simply by creating a function from $f(\langle M \rangle, x) = (M')$ Thus,...
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Is the Rice's theorem applicable to $\{ \langle M \rangle \mid M \mbox{ is a Turing machine such that }L(M) = H_{all} \mbox{ } \}$?

Until just now I thought that I have fully understood Rice's theorem but this example irritates me: $L^* = \{ \langle M \rangle \mid M \mbox{ is a Turing machine such that }L(M) = H_{all} \mbox{ } \}...
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Why is “accepted by Turing Machine with even number of states” a trivial property?

$$ L = \left\{ \left< M \right>~\middle|~ \small{ \begin{array}{l} L(M)\text{ is recognized by a Turing Machine} \\ \text{having even number of states} \end{array} } \right\}. $$ Isn't $L$ same ...
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Proving that a class of languages is a subset of RE for Rice Theorem

Consider language $L = \{<M> |L(M) \subseteq L(0(0\cup1)^*) \}$ where $<M>$ is a valid encoding of a turing machine. I know that the language is applicable for Rice Theorem. Now, I ...
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The bounded halting problem is decidable. Why doesn't this conflict with Rice's theorem?

One statement of Rice's theorem is given on page 35 of "Computational Complexity: a Modern Approach" (Arora-Barak): A partial function from $\{0,1\}^*$ to $\{0,1\}^*$ is a function that is not ...
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What is the definition of a property?

I have seen 2 answers in stackoverflow: A "trivial" property is one that holds either for all languages or for none. The property is trivial if it contains every TM, or if it is empty. My problem is:...
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Is undecidability of TMs' properties a statistical statement?

We know (by Rice's theorem) that is it not possible to decide a non-trivial property of a given TM. We could say therefore that we cannot be sure at 100 percent that a given TM has a certain non-...
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Rice's Theorem for Total Computable Functions

Fix a Gödel numbering, and write $\phi_n$ for the function coded by $n$. Rice's theorem states that if $P$ is the set of partial computable functions, and $A \subseteq P$, then the decision problem ...
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Reduction without Rice's Theorem

How can I show that the following language is neither semi decidable nor co-semi decidable without using Rice's Theorem? Further for the following language, how would I show that it IS co-semi ...
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RICE theorem applications

I am having some confusion in understanding RICE's theorem. It says every non trivial property of RE in undecidable. I need to understand when to apply RICE's theorem and when to not. Questions ...
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How to determine enumerability after applying Rice's theorem?

To my knowledge, lots of languages can be classified as undecidable after applying Rice's theorem, for example {"M" | L(M) is regular}. But what I am not sure is, how to determine if a language is ...
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Decide the set of all Turing machines with $L(M)=\left\{\langle M\rangle\right\}$

How can I prove that the language $L=\left\{\langle M\rangle\mid L(M)=\left\{\langle M\rangle\right\}\right\}$ is not decidable? When trying to use a diagonal argument, I cannot conclude from $L(M)\...
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Is the Rice Theorem applicable for these problems?

I have 1 problem :--> L = { < M > | TM halts on no inputs } I have solved the above problems by reductions given in the book and even there are many links ...
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Is the given language decidable?

L = { < M > | M is a turing machine and } Obviously, the language which L(M) is polynomially reducible to, is context free and hence recursive, so it is a decidable language . Now, L(M) is ...
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Does Rice theorem imply that it is not possible to find out the absolute optimum of a physical process?

One of my friends works for a big oil rafinery. He's in charge of optimising the inputs (volumes, maximum price to pay for crude oil etc.) given a profit. He's telling me there are heuristic ways to ...
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Prove whether this problem is decidable or undecidable [duplicate]

So I am reviewing my notes for this problem, and I cant seem to understand how this problem works. Say we have M, and M accepts an input that makes it visit every non-halting state. I convinced ...
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Use Rice's theorem to prove the following is undecidable

Given the language $L=\{\alpha \mid M_{\alpha}(x)=x^3$ for all $x\in\{0,1\}^*\}$. Prove using Rice's theorem that $L$ is undecidable. Rice's theorem: Let $P$ be a set of all computable functions $f:\...
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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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What is the meaning of undecidability in Rice Theorem?

Rice theorem says every non-trivial property of languages of Turing machines is undecidable. what is the meaning of undecidability here? is it semi-decidable? As an example the following language is ...
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Using Generalized Rice's Theorem to Prove Decidability

I have a Turing Machine M with a binary alphabet {1,2} that accepts a language L(M) that has infinitely many strings that start with 1 and finitely many strings that start with 2. I'm trying to ...
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Rice's Theorem: implication of having an undecidable property

I understand the assumptions that have to be true about a property or set of properties in a Turing machine description for Rice's Theorem to apply. But then what? If a set of Turing machines have ...
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Rice's theorem vs Turing completeness

I would like to clarify this because I see some kind of contradiction between Rice's theorem and Turing completeness. This is the problem: In building an Universal Turing Machine to emulate another ...
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What's a trivial property?

I have to show a property P is trivial. This problem has to do with Rice's Theorem, which I do not completely understand. Can someone explain the difference between trivial and non-trivial properties?...
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Rice Theorem - What is non-trivial property? [duplicate]

Every nontrivial property of the recursively enumerable languages is undecidable. What exactly is nontrivial property?
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Use Rice's theorem to show that the language of optimisable Turing machines is undecidable

I have an assignment to do and I'm quite stuck with the following question : Use Rice's theorem to show that $ \qquad L' = \{ \langle M \rangle \mid \; (\exists \text{ TM } M') \; [ L(M') = L(...
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Perplexed by Rice's theorem

Summary: According to Rice's theorem, everything is impossible. And yet, I do this supposedly impossible stuff all the time! Of course, Rice's theorem doesn't simply say "everything is impossible". ...