instruction stringlengths 0 29.8k ⌀ |
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I think you might be referring to [Sequitur](http://sequitur.info/).
**Edit** It has been suggested by other commenters that I leave more information for posterity. Fair point.
Sequitur is an algorithm by Craig Neville-Manning and Ian Witten (of _Managing Gigabytes_ fame). It's linear time in the size of the inpu... |
null |
Given the clarification to the question, it is a 0-1 knapsack problem (your knapsack is the money available, the value is the objective function), and look for ways to solve that one, for example following the [Wikipedia lead][1].
**Edit:** A simple approximate algorithm would be just sort equipment on increasing c... |
I wonder if two famous (and, IMHO, very nice) recreational problems are been studied in some general form.
Here's the first.
We have 13 balls, all looking absolutely the same, with 12 of them having the same weight; we don't know whether the ball that has a different weight is heavier or lighter. We have a balance ... |
On the generalization of two recreational problems: request for references, if there's any |
|reference-request|combinatorics| |
Short answer: the wrong thing in your solution is that the definition you are using does not give an $\mathsf{NL}$ algorithm, it gives an $\mathsf{NP}$ algorithm.
Here is another way to explain the problem: in $\mathsf{NL}$ you can't really assume that you get a witness to verify which is of polynomial size (as we d... |
The first problem is well-known. Lots of different generalizations appear in [this paper][1], which is listed in the Wikipedia entry on the [12 coins problem][2].
I've never heard of the second problem, but it is similar in spirit to the carrom board puzzle (which probably goes under other names as well), described ... |
Sometimes the master theorem is only given for recursions of the form $T(n) = aT(n/b) + \Theta(n^k)$, but the [Wikipedia article][1] includes a more general version which can handle functions of the form $T(n) = aT(n/b) + \Theta(n^k(\log n)^l)$, and even more general ones when $k \neq \log_b a$. The similar [Akra-Bazzi... |
I wonder where those terms came from.
Is it computer science related?
Or are they related to civil engineering, or swimming sports? |
Where did the terms memory pool and memory leak come from? |
|terminology| |
I wonder where those terms came from.
Is it computer science related?
Or are they related to civil engineering, or swimming sports?
Is it some analogy with filling water in a pool, or something like that? |
Is it possible to design a Universal Turing Machine in which the simulation time of a given Turing Machine $M$ is bounded by a factor of $\mathcal{O}(\log|\Gamma|+\log|Q|)$ of the original running-time of $M$, where $\Gamma$ and $Q$ are the tape alphabet and states of $M$ respectively?
If so, how can this be done? |
When I am reading a paper I found a notation $poly(|F|,n,$$\frac{1}{\epsilon}$) .
Its not clear for me that what this notation represents. Can you please help me out.
thank you. |
Notation Meaning |
|algorithm-analysis|randomized-algorithms|learning-theory| |
I'm a pure mathematician interested in learning about information theory. Unfortunately, I'm about as pure as they come - my specialty is mathematical logic, and I have absolutely no experience with programming or anything of a computational nature. I tried looking at Shannon's original paper, but the profusion of numb... |
Information theory from a (very pure) mathematician's perspective |
|information-theory| |
$\mathrm{poly}(\cdot)$ is simply notation for a function that is polynomial with respect to its parameters. In your case it would be polynomial in terms of $|F|$, $n$, and $\frac{1}{\epsilon}$. |
$F=poly(n)$ means that $F$ is polynomial in $n$, i.e., that there exists a constants $c$ such that $F=\Theta(n^c)$. (sometimes it might mean upper-bounded by polynomial, that is $F=O(n^c)$)
For multiple variable, the same applies, $poly(n,m)$ means polynomial both in $n$ and $m$, that is, there are constants $c_1,c_... |
I am familiar with asymptotic notations like Big-O ,little-o. But while I am reading some papers people are using the notations like $2^{O(d)}$ , $O(\epsilon^{1/2^d})$, $O(d)^d$ etc. I couldn't understand these notations properly. Is there any way (Lecture notes or video lectures with examples) to understand these thin... |
asymptotic notations |
|algorithms|time-complexity|asymptotics| |
That syntax is actually rather questionable formally, since it treats the big-O as a function, which it is not. But with a bit of slop the rule to interpret these is rather simple. The big-O stands for some function with the asymptotic behaviour given by the big-O.
I'll start with the full syntax of the big-O notati... |
$F=\mathrm{poly}(n)$ means that $F$ is polynomial in $n$, i.e., that there exists a constants $c$ such that $F=\Theta(n^c)$. (sometimes it might mean upper-bounded by polynomial, that is $F=O(n^c)$)
For multiple variable, the same applies, $\mathrm{poly}(n,m)$ means polynomial both in $n$ and $m$, that is, there are... |
null |
|terminology|asymptotics|landau-notation| |
It can be the case that *there is no proof of $\mathsf{P} = \mathsf{NP}$ and no proof of $\mathsf{P} \ne \mathsf{NP}$*. Hence there will be no algorithm to decide whether $\mathsf{P} \overset{?}{=} \mathsf{NP}$.
So we don't kniw if there is a proof for $\mathsf{P} = \mathsf{NP}$ or $\mathsf{P} \neq \mathsf{NP}$, le... |
null |
Yes, Computer Science.
Back in the days of the NASA/Apollo program (and possibly before), mainframe computers had wads of memory (like as much as 256 Mwords). To support multi-tasking, a program/task running on that mainframe had to specify how much memory was required to do its job, and the system would allocate th... |
I am familiar with asymptotic notations like Big-O ,little-o. But while I am reading some papers people are using the notations like $O(\epsilon^{1/2^d})$, $O(d)^d$ etc. I couldn't understand these notations properly. Is there any way (Lecture notes or video lectures with examples) to understand these things clearly.
... |
That syntax is actually rather questionable formally, since it treats the big-O as a function, which it is not. But with a bit of slop the rule to interpret these is rather simple. The big-O stands for some function with the asymptotic behaviour given by the big-O.
I'll start with the full syntax of the big-O notati... |
Need a suggestion >>Which is the best technique for Online Character Recognition,
PCA or SVM or if you want to add anything new.
Actually i want to detect the motion of the finger so that if someone writes something infront of the camera in the air ,i want to recognize the characters online(meaning as soon as they a... |
Best Technique for Handwritten Character Recognition |
|computer-vision| |
What you describe is a whole research field, and IMHO a bit out of scope here, but I'll try to provide some pointers anyway.
You should be able to find some review papers on [Google scholar](http://scholar.google.com/) that can help you deciding on a technique to use.
Personally I would advise that you divide ... |
null |
|terminology|reference-request|data-structures|lists| |
On Facebook HackerCup 2013, they asked the following question:
> Your friend John uses a lot of emoticons when you talk to him on
> Messenger. In addition to being a person who likes to express himself
> through emoticons, he hates unbalanced parenthesis so much that it
> makes him go :(
>
> Sometimes he puts ... |
|algorithms|optimization| |
|terminology|algorithm-analysis| |
When I am reading a paper I found a notation $\operatorname{poly}( |F|,n,$$\frac{1}{\epsilon}) $.
Its not clear to me that what this notation represents. Can you please help me out? |
What is meant by $poly(|F|, n, e)$? |
|terminology|history| |
I need a suggestion. Which is the best technique for Online Character Recognition,
PCA or SVM or if you want to add anything new.
Actually I want to detect the motion of the finger so that if someone writes something in front of the camera in the air, I want to recognize the characters online (meaning as soon as t... |
|reference-request|machine-learning|computer-vision|pattern-recognition| |
So say I have a task like this:
> Construct a Turing machine transforming the word u to the word v byt
> removing all the sequences of form "ba" from the word u. Input
> alphabet = {a,b,c}.
> Example: for IN cabbaacba, OUT cac.
And my problem always is: can I leave blank characters in place of "ba" sequence... |
Clarification for a class of Turing machine problems |
|turing-machines| |
null |
Can GDB be run on itself? How or why not?
I see something about it http://www.math.utah.edu/docs/info/gdbint_3.html
But GDB might not be written in a language that it can debug? |
Can GDB debug itself? |
|correctness-proof|program-correctness| |
I find this a bit difficult to describe, but I am interested in the following idea :
The LZ algorithm factors (verb) an input stream into adjacent factors, these are by definition the maximal prefixes of the piece of text that occur in the previous text (or equivalently the previous concatenation of LZ factors).
... |
Theoretical question about Lempel-Ziv 77 |
|algorithms|formal-grammars|combinatorics| |
Obtain the source code for gdb.
Compile with the `-g` flag on.
Run `gdb gdb`. |
What you describe is a whole research field, and IMHO a bit out of scope here, but I'll try to provide some pointers anyway.
You should be able to find some review papers on [Google scholar](http://scholar.google.com/) that can help you deciding on a technique to use.
Personally I would advise that you divide ... |
Alan Turing's paper [*On computable numbers, with an application to the Entscheidungsproblem*][1], 1936 is an extremely important paper (it started the entire field, one could say), and it's also a pleasant read. Highly recommended reading.
Claude Shannon's paper [*A mathematical theory of Communication*][2], 194... |
Yes, it's possible. Here's how to do it.
1. Obtain the source code for gdb.
2. Compile with the `-g` flag on.
3. Run `gdb gdb`. |
I am studying formal language theory and have been asked to prove the following:
$\forall L, L^*=(L^*)^*$
I've started with
$def. L^* = \bigcup_{i \in \mathbb{N}} L_i, L_0=\{{\epsilon}\}, L_1=\{L\}, L_{i+1}=\{uv|u\in L_i, v\in L\}$
$then (L^*)^* = \bigcup_{i \in \mathbb{N}} L_i^*, L_0^*=\{{\epsilon}\}, L_1^... |
Experimenting with applying LZ77 to input. Naively (O(n**2) runtime, infinite window) LZ77 is the following :
def lz77(s):
lens = len(s)
factors = []
i = 0
while i < lens:
max_match_len = 0
current_word = i
... |
Behavior of iterative application of LZ77 |
|formal-grammars| |
The question isn't very clear, but it seems that you are trying to use a neural network to analyze a pseudo random number generator (PRNG). The idea being that if the values are properly random, the network won't learn anything, and if it will, then the random number generator is flawed.
If this is the case, I don'... |
> **Problem:** Consider a Graph $G=(V,E)$ with $n$ vertex and $m>n$ edges, $u$ and $v$ are two vertex of $G$ and $(u,v) $ is the edge with minimum weight in G.
>What is the asymptotic complexity of calculate the shortest path from $u$ to $v$ with Djkstra's Algorithm using [Binary Heap](http://en.wikipedia.org/wiki/B... |
Algorithm exercise |
|asymptotics|shortest-path| |
Lempel and Ziv proved that under some reasonable assumptions, the limiting rate of their algorithm is equal to the entropy of the text. That means that in the limit, the output should be completely random. Random text cannot be compressed (on average), so you should expect that if you take a long text and apply Lempel-... |
The question does not mention replacing "ba" by spaces. It does not say that you can have spaces between the symbols in the output word. Is the blank character even in the output language?
|
> **Problem:** Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$ and $(u,v)$ is the edge with minimum weight in $G$.
>What is the asymptotic complexity of calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using [Binary Heap](http://en.wikipedia.o... |
null |
null |
Number of swaps < Number of iterations (in both optimized as well as simple bubble case scenario)
Number of Inversions = Number of swaps.
Therefore,
Number of Iterations > $\frac{n(n-1)}{4}$
Thus, Average case complexity is $\omega(n^2)$.
But, since average case cant exceed worst case, we get that it is $... |
So I'm doing some exercises with Turing machine and quite often it happens that a given set of states can be achieved if and only if some character was met. Therefore, we may have some states q3-q7 which the machine may be pointed to if and only if we spotted a and (because of the task spec, for example), we know that ... |
Are you allowed to have empty states on Turing machine? |
|turing-machines| |
> **Problem:** Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$ and $(u,v)$ is the edge with minimum weight in $G$.
>What is the asymptotic complexity to calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using [Binary Heap](http://en.wikipedia.o... |
|algorithms|graphs|algorithm-analysis|runtime-analysis|shortest-path| |
> **Problem:** Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$ and $(u,v)$ is the edge with minimum weight in $G$.
>What is the asymptotic complexity to calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using [Binary Heap](http://en.wikipedia.o... |
What's the complexity of calculating the shortest path from $u$ to $v$ with Dijkstra's algorithm using binary heap? |
I am looking for algorithms to prioritize equipment renewals.
Input: (years since last renewal, cost of renewal, importance of renewal).
Output: An ordering of the equipment according to which it will be renewed.
I do not know if there are any algorithms for this particular problem. If you have any idea how to... |
Algorithms to prioritize equipment renewals |
What is meant by $\operatorname{poly}(|F|, n, e)$? |
> **Problem:** Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$.
>What is the asymptotic complexity to calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using [Binary Heap](http://en.wikipedia.org/wiki/Binary_heap) ?
**My idea:**
Dijks... |
Your answer actually depends on what implementation of Dijkstra's algorithm is used. The textbook implementation inserts all nodes in the queue, and then proceeds with the extraction. The other starts with only the source in the queue. This is generally more efficient in practice, although it needs a bit of book-keepin... |
> **Problem:** Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$.
>What is the asymptotic complexity to calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using [Binary Heap](http://en.wikipedia.org/wiki/Binary_heap) ?
To clarify, Dijkstra's al... |
Your answer actually depends on what implementation of Dijkstra's algorithm is used. The textbook implementation inserts all nodes in the queue, and then proceeds with the extraction. The other starts with only the source in the queue. This is generally more efficient in practice, although it needs a bit of book-keepin... |
As part of my homework I need to prove or disprove that changing the contrast and than changing the brightness is, or isn't the same as changing the brightness and after that changing the contrast.
let's assume that we are using gray-scale.
brightness - is the mean of the the gray levels.<br>
changing brightness... |
Contrast vs. Brightness question |
|image-processing| |
Write down brightness and contrast as functions that act on a single gray-scale pixel. As you said, brightness is $b(x) = x + \alpha$ and contrast is $c(x) = \beta(x - x_\text{mean}) + x_\text{mean}$ or something similar. Now all you need to show is that $b \circ c \neq c \circ b$. |
For a language $L$ with pumping length $p$, and a string $s\in L$, the pumping lemmas are as follows:
**Regular version**:
If $|s| \geq p$, then $s$ can be written as $xyz$, satisfying the following conditions:
1. $|y|\geq 1$
2. $|xy|\leq p$
3. $ \forall i\geq 0: xy^iz\in L$
**Context-free version**:
If $|... |
Can someone explain succintly how the pumping lemmas necessitate their first two conditions? |
|regular-languages|context-free|pumping-lemma| |
It is a typical example of a [space-time tradeoff][1] trading increased time (CPU instructions required) for decreased space (memory required). There are many examples of this.
In this particular case I'd say it is a (simple) form of lossless [compression][2]. This because the data is stored in a minified but unusab... |
I think you are looking for the topic of "**Algorithmic Information Theory**". This site contains lots of information about this topic: http://www.hutter1.net/ait.htm |
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