# Questions tagged [complexity]

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### Turing Machine that stops after certien steps question

Let A be a decision problem such that: A = {(M,x) | M turing machine that accepts x in 2^|x| steps} show that A not in P. How could I prove that A is not in P, I tried doing so using NL but I thought ...
1 vote
73 views

### Cheapest Insertion is $2$-approximation for TSP

Consider the Cheapest Insertion Algorithm on a complete graph with $n$ vertices, where each edge $uv$ has a weight $w(uv)$, and the weights satisfy the triangle inequality $w(xz)\leq w(xy)+w(yz)$ for ...
68 views

### Direct fpt reduction from Weighted 3SAT to Weighted 2SAT

In parameterized complexity, for each fixed $q$, the problem Weighted $q$-CNF SAT is W-complete. In particular, this means that one can turn a 3CNF formula $\varphi$ into a 2CNF formula $\varphi'$ ...
130 views

### Validity problem of intuitionistic two-variable logic

The two-variable fragment $\mathrm{FO}^2$ consist of those sentences of first-order logic $\mathrm{FO}$ in which precisely two variables occur (e.g. $\exists x \exists y \exists z R(x,y,z)$ is not a ...
176 views

### Any problems for which we know the complexity, but no algorithms with the same time?

I suddenly found myself wondering if there are any problems for which the complexity (time or space or anything else) is proven, say to be O(n^2), but for which the best known algorithms are worse ...
86 views

### Recursive generic oracles

In Fenner, Stephen; Fortnow, Lance; Kurtz, Stuart A.; Li, Lide, An oracle builder’s toolkit, Inf. Comput. 182, No. 2, 95-136 (2003). ZBL1025.68041, the authors go through a variety of generic oracles. ...
1 vote
144 views

### Is QMA known to contain Co-NP?

Is QMA known to contain Co-NP? If not, would Co-NP being contained in QMA have any implications for other complexity classes. (e.g. Causing the polynomial heirachy to collapse.)
241 views

1 vote
71 views

### Sentences in what kinds of grammar in the Chomsky hierarchy can be parsed by an LSTM of a given size?

Given an LSTM $N$ of a given size $A$, a sentence $S$ with a given number of words $B$, a Chomsky grammar hierarchy level $C$ in 0-3, a Chomsky grammar $G$ of level $C$ of size $D$, A given fixed, ...
70 views

### Looking for Research in Cryptographic Computing

I recall reading in college about a nascent research area regarding cryptographic techniques for secure computing, relating to zero-knowledge proofs, but I am having trouble remembering the exact term....
191 views

### SAT Solvers and their applications

I've been reading and learning about SAT solvers this week. If they can solve problems with thousands of variable quickly haven't we practically solved ANY problem that can be reduced to it, including ...
433 views

### Is there a counterexample to this work?

Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However ...
379 views

### Error in paper "Some NP-complete geometric problems"?

The paper in question: M.R. Garey, R.L. Graham and D.S. Johnson. Some NP-complete geometric problems . This paper proofs the NP-completeness of some well-known problems, such as the Steiner Tree ...
218 views

### Paths of length $p$ in a Graph, $p$ a prime

I came across the following decision problem, for which I wondered whether anybody of you came across a similar problem and can give me some insight on its nature/complexity. Given as input a ...
### Implications of resolving $BPP$ vs $PSPACE$
The relationship between the complexity classes $BPP$, $P$, and $NEXP$ is currently undetermined. We know that $P \neq EXP$ by the time hierarchy theorem, but we don't know if $BPP = P$ (as many ...