Questions about problems which cannot be solved by any Turing machine.
Questions tagged [undecidability]
882 questions
8
votes
1 answer
Problem complete for the class of ALL languages
$\text{ALL}$ is literally the class of ALL languages.
Are there $\text{ALL}$—complete problems? That is, are there problems for which a solution would allow one to solve any problem whatsoever? Such problems could reasonably be considered"the…
Demi
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7
votes
1 answer
Are there problem instances which we know to be unsolvable?
As it says in the title:
Are there problem instances which we know to be unsolvable?
Or equivalently
Are there any promise problems with a finite number of possible inputs
which are undecidable?
Please note:
I realize that many computational…
guest_56763556765
- 71
- 1
7
votes
1 answer
Reduction to a parameterized problem
I'm trying the following question from my homework:
We're given a graph $G$ and parameters $k,\hat{P}, \hat{W}\in \mathbb{N}$. Additionally, each $v \in V(G)$ has a profit and weight: $p_v, w_v\in \mathbb{N}$.
Suppose you're given an $f(k) \cdot…
Chi Pong
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4
votes
1 answer
Hierarchy of undecidable languages
Let us define two languages of Turing machines.
$$
EQ_{TM} = \{ : L(M_1) = L(M_2)\}
$$
$$
ALL_{TM} = \{ : L(M) = \Sigma^*\}
$$
It is easy to show that neither of the languages are in $RE \cup coRE$, and also it is easy to construct a…
Igor Shinkar
- 241
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3
votes
2 answers
Infinite languages and undecidable languages
I'm having a problem with proving the following statement:
For every infinite language $L$, does there exists an infinite language $L' \subseteq L$ such that $L'$ is not decidable?
tom
- 31
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3
votes
0 answers
Hamming connectivity of regular languages
Call a language $L$ Hamming connected iff, for every pair of strings $x, y \in L^2$, where $|x|=|y|$, $x$ may be transformed into $y$ by a sequence of single symbol in-place replacements, so that after every replacement, the resulting string is in…
Skynet_0
- 131
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3
votes
1 answer
How post correspondence problem is undecidable?
An undecidable problem is a problem that cannot have any algorithm to solve it.
Post correspondence problem can be solved using a brute force approach. Then how can it be an undecidable problem?
hanugm
- 505
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2
votes
0 answers
The decidability of a problem involving univariate integer polynomials
Suppose that we are given $f_1(x),...,f_n(x) \in \mathbb{Z}[x]$. Decide whether there exist $a_1,...,a_n \in \mathbb{Z}$ such that
$\sum_{i=1}^{n} a_if_i(x) = p(x)^2 $
$p(x) \in \mathbb{Z}[x]$.
In other words, decide whether there are integer…
Kevin
- 168
- 5
2
votes
1 answer
Deciding whether the language of a CFG equals some specific regular language
I was wandering if $L = \{\langle G \rangle \mid \ G \text{ is a context free grammar and } \mathcal L(G) = A \}$ is decidable where A is a some regular language. Is
$L' = \{ \langle G \rangle \mid \ G \text{ is a context free grammar and }…
user66505
- 21
- 1
2
votes
1 answer
Why can't configuration counting decide undecideable problems?
I know it might sound like a silly question, I just can't get my head around it...
I just read that $DSPACE(f(n))\subseteq DTIME(n\cdot 2^{O(f(n))})$.
The proof for it relies heavily on the fact that for a given $L\in DSPACE(f(n))$, the turing…
so.very.tired
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2
votes
0 answers
Help me verify my proof that FINITE is undecidable
Is my proof that FINIT is undecidable correct?
FINITE= { ⟨M⟩ | M is a Turing machine that accepts only finitely many strings } is undecidable.
Answer:
To prove this we can use reduce to Halting Problem, which is a known to be undecidable problem.
to…
Sachihiro
- 121
- 2
2
votes
2 answers
Undecidable languages
I'm confused on the definition of undecidable languages.
Definition: For an undecidable language, there is no Turing Machine which accepts the language and makes a decision for every input string w.
Can you say a language that isn't recognizable as…
ss sss
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2
votes
1 answer
To check whether the problem of a particular string being a member of CFG G is decidable or not, why can't we use a PDA?
Why can't a TM simulate a PDA? Then we can easily construct a PDA P which is made from grammar G. And contruct a TM that simulates P to prove that this problem is decidable.
Eesh Starryn
- 143
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2
votes
1 answer
PCP with commutative alphabet
Post's Correspondence Problem is known to be undecidable. A variant of PCP, namely PCP with partially commutative alphabets is also known to be undecidable.
Is the following variant also known to be undecidable?
PCP with commutative alphabet.
Given…
Umang
- 41
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1
vote
2 answers
Is this a correct decider?
We are given the following language
B = {$$ : M is a turing machine and $i \in \mathcal{N}$ and M accepts some string in atmost $i$ steps }
Is language B decidable ?
As per a hint from another fellow user, I decided to construct the following…
rajaditya_m
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