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Canonical forms for unlabeled unrooted trees |
|trees| |
null |
|optimization|reductions|reference-request|satisfiability|boolean-algebra| |
I'm not sure if I'm posting in the correct section, but I wanted to learn about CDVs, how the weightings work, and the computation.
I'm reviewing how a system is configured and looking to add a new range of numbers, but it fails validation, someone mentioned that it's probably linked to the weightings.
The CDV is... |
Help with understanding Check Digit Validations |
|algorithms| |
Consider the language $ALL_{NFA} = \{\langle A\rangle: \text{$A$ is an NFA with $L(A) = \Sigma^*$}\}$.
If you want a non-PTIME reduction from $\overline{ALL_{NFA}}$ to $ALL_{NFA}$, then you can simply do the following naive approach. On input $\langle A\rangle$ for the reduction, the reduction checks whether $L(A) \... |
Consider the language $ALL_{NFA} = \{\langle A\rangle: \text{$A$ is an NFA with $L(A) = \Sigma^*$}\}$.
If you want a non-PTIME reduction from $\overline{ALL_{NFA}}$ to $ALL_{NFA}$, then you can simply do the following naive approach. On input $\langle A\rangle$ for the reduction, the reduction checks whether $L(A) \... |
null |
For the first term we simply use the word "state".
For the second term, using "state of the NFA" is confusing because we read it as "one of the NFA's states". If you are not sure which terminology to use, then you can state explicitly what you mean, or define a term clearly before using it.
So for an NFA $A = \lan... |
For the first term we simply use the word "state".
For the second term, using "state of the NFA" is confusing because we read it as "one of the NFA's states". If you are not sure which terminology to follow, then you can state explicitly what you mean, or define a term clearly before using it.
So for an NFA $A = \... |
null |
Consider the language $ALL_{NFA} = \{\langle A\rangle: \text{$A$ is an NFA with $L(A) = \Sigma^*$}\}$.
If you want a non-PTIME reduction from $\overline{ALL_{NFA}}$ to $ALL_{NFA}$, then you can simply do the following naive approach. On input $\langle A\rangle$ for the reduction, the reduction checks whether $L(A) \... |
Given an $n \times n$ matrix of integers, I would like to find the optimal dividing line that maximizes the sum of the integers on the same side as the top left corner. The dividing line should be connected and made up of only vertical and horizontal parts. For example:
[![enter image description here][1]][1]
... |
Maximum sum staircase complexity |
|algorithms| |
null |
Say I have N points sampled on a surface in 3 dimensions (ie. points on the surface of a sphere, 1-torus etc.). Is there an algorithm that would be able to count the number of holes in the surface formed by those point (ie. zero holes for the sphere, 1 hole for the 1-torus etc)? |
How to topologically classify points in 3d space generating a surface? |
|computational-geometry|topology| |
null |
Under mod 2 arithmetic ($\mathbb{Z}$={0,1}), given a set $V$ of $n$x$1$ linearly independent vectors $\{x_1,...,x_n\}$ I'd like to find a $n^2$ binary matrix $M$ such that $Mv=v$ where $v \in V$ and $M\bar{v}\neq \bar{v}$ for $\bar{v}\not \in V$.
I supposed it would also be helpful to know the technical term for a ... |
To get the best performance you need to measure: What is the time for one request requesting n rows? Quite often there is a fixed time per request, plus a much smaller time for any item of data.
With that information you can for example request the data you need plus some extra data if you expect the user might scr... |
It is not possible. Such matrices don't exist. We always have $Mv=v$ whenever $v=0$ (the all-zeros vector). No set that contains the all-zeros vector is linearly independent, so surely $0 \notin V$. Therefore, no matter what $M$ you choose, when we set $v=0$, we discover $Mv=v$ for some $v \notin V$, which violates... |
Given an input NFA, can one construct an NFA that is universal (that is, accepts all its inputs) if and only if, the input NFA isn't universal?
I tried to use the fact that NFA-universality is PSPACE-complete, and the fact that PSPACE = coPSPACE. I am also interested in the details of a simple construction. |
|complexity-theory|finite-automata|space-complexity|nondeterminism|polynomial-time-reductions| |
null |
null |
There are many possible algorithms for checksums and "check digits". We can't answer those questions without knowing which one is being used in your setting.
I suggest doing some more background reading on the subject. See, https://en.wikipedia.org/wiki/Check_digit, https://en.wikipedia.org/wiki/Checksum, https://... |
Under mod 2 arithmetic ($\mathbb{Z}$={0,1}), given a set $V$ of $n$x$1$ linearly independent vectors $\{x_1,...,x_n\}$ I'd like to find a $n^2$ binary matrix $M$ such that $Mv=v$ where $v \in V$ and $M\bar{v}\neq \bar{v}$ for $\bar{v}\not \in V$.
I supposed it would also be helpful to know the technical term for a ... |
Could someone explain to me, through an example, how the McNaughton–Yamada–Thompson algorithm works in a way that I can understand?
Thank you in advance for your helpful response! |
How to work thompson's construction algorithm? |
|finite-automata|regular-expressions| |
Dominating set: given a graph G and an int k, is there is a dominating set of size k in G?
Disconnected dominating set: same as above, but the dominating set has more than one connected component |
Reduction from dominating set to disconnected dominating set |
|np-complete|reductions|np-hard|polynomial-time-reductions| |
null |
One of the standard exercises in automata theory is to show that going from an NFA $A$ to a complementing one involves an exponential blow-up. Here is one way to do it:
Consider the alphabet $\Sigma = \{ 0, 1\}$, and for every $n\geq 1$, consider the language $$L_n = \{ w\in \Sigma^*: w \text{ has an infix }u \in 0... |
One of the standard exercises in automata theory is to show that going from an NFA $A$ to a complementing one involves an exponential blow-up. Here is one way to do it:
Consider the alphabet $\Sigma = \{ 0, 1\}$, and for every $n\geq 1$, consider the language $$L_n = \{ w\in \Sigma^*: w \text{ has an infix }u \in 0... |
One of the classical ideas in automata theory is showing that going from an NFA $A$ to a complementing one involves an exponential blow-up. Here is one way to do it:
Consider the alphabet $\Sigma = \{ 0, 1\}$, and for every $n\geq 1$, consider the language $$L_n = \{ w\in \Sigma^*: w \text{ has an infix }u \in 0 \c... |
In my opinion, monographs on approximation algorithms come closest to what you are seeking:
- [Complexity and Approximation][1], by Giorgio Ausiello et al.
- [Approximation Algorithms][2], by Vijay Vazirani,
- [The Design of Approximation Algorithms][3], by David Williamson and David Shmoys.
If you are st... |
Consider an undirected graph $G = \langle V, E\rangle$, and consider a dominating set $S\subseteq V$ in $G$. If you mean by "$S$ is disconnected" that the subgraph induced by $S$ is not strongly connected, then the following is a trivial reduction from dominating set:
On input $\langle G, k\rangle$, the reduction o... |
One of the classical ideas in automata theory is showing that going from an NFA to a complementing one involves an exponential blow-up. Here is one way to do it:
Consider the alphabet $\Sigma = \{ 0, 1\}$, and for every $n\geq 1$, consider the language $$L_n = \{ w\in \Sigma^*: w \text{ has an infix }u \in 0 \cdot ... |
Dominating set: given a graph G and an int k, is there is a dominating set of size k in G?
Disconnected dominating set: same as above, but the dominating set has more than one connected component
I was suggested to duplicate G |
Dominating set: given an undirected graph G and an int k, is there is a dominating set of size k in G?
Disconnected dominating set: same as above, but the subgraph induced by the dominating set is disconnected
I was suggested to duplicate G |
It can be solved in $O(n^2 k)$ time using dynamic programming. Let $A[1..n,1..n]$ be the matrix. Define $T[i,j,\ell]$ be the maximum possible sum of the top-left corner, for any dividing line that divides $A[i..n,j..n]$ using at most $\ell$ horizontal parts. Then there is a simple recurrence relation for $T[i,j,\ell... |
|finite-automata|nondeterminism|lower-bounds| |
null |
null |
null |
You can compute the maximum weight of an antichain, or more generally the maximum weight of a union of $k$ antichains, by reducing to the maximum flow problem. See for example the following technical report by Cong:
[Computing Maximum Weighted K-Families and K-Cofamilies in Partially Ordered Sets](http://ftp.cs.ucla... |
null |
The paper [*The Parameterized Complexity of Local Consistency*](http://link.springer.com/10.1007/978-3-642-23786-7_24) by Gaspers and Szeider discusses coW[1]- and coW[2]-complete problems. This is maybe a starting point. |
If another thread has modified the logical memory belonging to that cache line then there will be a delay.
It is unlikely that the processor can move data directly from one private cache to another. So if the data is changed in processor B’s private cache, that processor needs to be notified, then it writes the cac... |
Say I have N points sampled on a surface in 3 dimensions (ie. points on the surface of a sphere, 1-torus etc.). Is there an algorithm that would be able to count the number of holes in the surface formed by those point (ie. zero holes for the sphere, 1 hole for the 1-torus etc)?
As a constraint, the points that make... |
Say I have N points sampled on a surface in 3 dimensions (ie. points on the surface of a sphere, 1-torus etc.). Is there an algorithm that would be able to count the number of holes in the surface formed by those point (ie. zero holes for the sphere, 1 hole for the 1-torus etc)?
Edit:
As a constraint, the points th... |
I want to make a Galaxy schema of a Restaurant. There are 2 fact tables sales and purchases. sales are related to customer and purchases to supplier of ingredients.
Now my question is how can i make galaxy schema
and from where i can find large dataset for my dataware house project |
Restaurant Galaxy schema |
|database-theory|data-mining| |
null |
You are looking for [persistent homology](https://en.wikipedia.org/wiki/Persistent_homology), a branch of computational topology that studies precisely the question you asked.
Roughly, the idea is as follows. Pick a "resolution radius $r$", draw a ball of radius $r$ around each sample point, and compute the resultin... |
null |
I have been stuck on a task in class. I have to find a context-sensitive grammar for the language $L=\{a^{n}b^{2^{n}}|n \in \mathbb{N}\}$ and I just cannot figure it out. Any help would be very much appreciated! |
context-sensitice grammar for a language |
|formal-languages| |
null |
I was [watching a presentation](https://www.youtube.com/watch?v=2xVN-qY78P4) related to the MuJoCo simulator (and other topics which were more relevant for the presentation itself) and at one moment in the presentation it is mentioned that MuJoCo has thread safety due to not having memory allocation in runtime.
Why ... |
Thread safety due to no runtime allocation of memory, why? |
|memory-management|simulation|threads| |
Let $N_A$ and $N_B$ be NFAs for the languages $A$ and $B$, respectively.
Note that $B\setminus A = B\cap \overline{A}$. Hence,
to obtain an NFA $N_C$ for $C = B\cap \overline{A}$, one needs to complement $N_A$, but you don't have to complement $N_B$ as the product construction for intersection can be easily adapted... |
TQBF is a canonically **PSPACE**-complete problem. It consists of boolean formula such that all its variables are quantified. The question is whether a given TQBF instance is TRUE or FALSE.
https://en.wikipedia.org/wiki/True_quantified_Boolean_formula
My query is regarding the formula part. No source explicitly m... |
Is TQBF problem where clauses are in 3-CNF format PSPACE-complete? |
|complexity-theory|space-complexity| |
null |
I’m definitely not a computer science expert, but I find this topic extremely interesting - due to this interest, I’ve recently enrolled in a class about Turing Machine.
The lecturer assigned to us an exercise and one of the questions is: ‘Write down a program of a Turing Machine with just two states that, when giv... |
How to write down a program of a Turing Machine with just two states that, when given the empty tape as inputs, halts after 6 steps |
|turing-machines| |
I'm currently working on a problem to come up with ideas to solve a stable flow problem but unlike the traditional stable flow problem where every node has preferences on its incoming and outgoing edges, I only care about preferences on outgoing edges. The paper ["Stable Flows over Time"][1] presents a nice simple solu... |
Stable Flow Problem with one sided preferences |
|decision-problem|network-flow|efficiency|matching|game-theory| |
In my PhD, I will work with ML models. However, I will only use ready-made models as a tool, but I want to delve deeper into Artificial Intelligence not just to use ready-made models, but to understand how it works and create my own AI.
I noticed that most of the content I found talked more about how to use ready-ma... |
Main subjects to learn Artificial Intelligence in CS |
|machine-learning|artificial-intelligence|reinforcement-learning| |
It is impossible, unless your professor defined the semantics of a Turing machine in a non-standard way. Or perhaps you meant two non-final states? Here is why:
Every Turing machine $M$ has at least two states: an accepting state $q_{acc}$, and a rejecting state $q_{rej}$. Whenever $M$ reaches $q_{acc}$ or $q_{rej}... |
{"Voters":[{"Id":77862,"DisplayName":"Bader Abu Radi"}],"DeleteType":1} |
It is impossible, unless your professor defined the semantics of a Turing machine in a non-standard way. Or perhaps you meant at most two non-final states? Here is why:
Every Turing machine $M$ has at least two states: an accepting state $q_{acc}$, and a rejecting state $q_{rej}$. Whenever $M$ reaches $q_{acc}$ or ... |
{"Voters":[{"Id":77862,"DisplayName":"Bader Abu Radi"}]} |
{"Voters":[{"Id":77862,"DisplayName":"Bader Abu Radi"}],"DeleteType":1} |
It is impossible, unless your professor defined the semantics of a Turing machine in a non-standard way, or perhaps you meant at most two non-final states? Here is why:
Every Turing machine $M$ has at least two states: an accepting state $q_{acc}$, and a rejecting state $q_{rej}$. Whenever $M$ reaches $q_{acc}$ or ... |
{"Voters":[{"Id":77862,"DisplayName":"Bader Abu Radi"}]} |
Consider an undirected graph $G = \langle V, E\rangle$, and a set $S\subseteq V$ of vertices. We say that $S$ is a *dominating set*, if for every vertex $v\in V$, it holds that $v\in S$, or $v$ has a neighbor in $S$. We say that $S\subseteq V$ is a *disconnected dominating set* if it is a dominating set and the subgrap... |
|graphs|np-complete|reductions|np-hard|polynomial-time-reductions| |
null |
It is impossible, unless your professor defined the semantics of a Turing machine in a non-standard way, or perhaps you meant at most two non-final states? Here is why:
Every Turing machine $M$ has at least two states: an accepting state $q_{acc}$, and a rejecting state $q_{rej}$. Whenever $M$ reaches $q_{acc}$ or ... |
null |
null |
They seem to believe that runtime memory allocation causes thread safety to be lost. But the only problem is that you need to synchronise allocation and deallocation of memory, so if two threads need the same memory at the same time, one allocates and the other waits until it has been allocated.
Once that memory is... |
When you shift, you don’t shift memory, you shift values. The result of shifting 0xffffff00 left by one bit position is the same whether the processor is bigendian or littleendian.
Shifting to the left by k bits multiplies by 2^k, shifting to the right divides by 2^k (roughly. Signed integers can be interesting). |
null |
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