Linked Questions

35 votes
7 answers

What are the simplest examples of programs that we do not know whether they terminate?

The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. ...
MaiaVictor's user avatar
  • 4,117
45 votes
2 answers

How to show that a function is not computable? How to show a language is not computably enumerable?

I know that there exists a Turing Machine, if a function is computable. Then how to show that the function is not computable or there aren't any Turing Machine for that. Is there anything like a ...
user5507's user avatar
  • 2,191
10 votes
4 answers

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 ...
ttbo's user avatar
  • 113
5 votes
2 answers

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?...
Alex Chumbley's user avatar
33 votes
1 answer

Rice's theorem for non-semantic properties

Rice's theorem tell us that the only semantic properties of Turing Machines (i.e. the properties of the function computed by the machine) that we can decide are the two trivial properties (i.e. always ...
Kaveh's user avatar
  • 22.2k
9 votes
4 answers

Implications of Rice's theorem

Every time I think I get what Rice's theorem means, I find a counterexample to confuse myself. Maybe someone can tell me where I'm thinking wrong. Lets take some non-trivial property of the set of ...
Stefan Lutz's user avatar
6 votes
2 answers

Are these sets of indices also index sets?

An index set is a set of all indices of some family of computably enumerable sets. It is known that the empty set is an index set and that $K = \{e \mid e \in W_e\}$ is not an index set. The ...
girlonbeach's user avatar
2 votes
1 answer

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(M) \...
Über Lem's user avatar
0 votes
2 answers

Prove the halting problem is undecidable using Rice's theorem

Is it possible to prove that the Halting problem is undecidable using Rice's theorem? Here's what I've tried and failed: We want to reduce Rice's Theorem (decide if a language has the nontrivial ...
an idiot's user avatar
0 votes
2 answers

How do I prove that a Turing Machine that accepts a string w in an even number of steps is not decidable?

Let a language A = {(M,w) : M is a TM and w is a string such that w is accepted by M in an even number of steps}. How can I prove that this is undecidable? I have considered trying to build the ATM ...
Ricardo Ferreira da Silva's user avatar
2 votes
2 answers

Does rice theorem applies to languages only or does it apply to machines as well?

Rice theorem says that any non trivial property of a language recognized by a Turing Machine is undecidable. Now does this theorem applies to machines as well since we can define a language ...
Kishan Kumar's user avatar
1 vote
1 answer

Is the set of Gödel numbers of computable constant functions recursively enumerable?

I've been working on the following exercise: $S = \{ x | f_x \text{ is constant} \}$. Is $S$ recursively enumerable? Here, $fx$ is the function computed by the $\text{x-th TM}$. So it is a ...
PALEN's user avatar
  • 317
-1 votes
2 answers

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 ...
Jerome's user avatar
  • 109
1 vote
1 answer

Proving that context-freeness of $L(M)$ is not semi-decidable using Rice's theorem

This is a question from an exam I did today: Given $M$, a turing machine, we need to decide the following: 1) $M$ halts on every input 2) The language of $M$ is CFL My question is, can I ...
TheNotMe's user avatar
  • 571
-1 votes
1 answer

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:\...
Andrew Brick's user avatar

15 30 50 per page