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Time units required for Interrupt Cycle |
|computer-architecture| |
As [AJed][1] mentioned, [ACM digital library][2] and [IEEE xplorer][3] would be near the top of list.
Additionally [Goggling with advanced search][4] for the name of the reference with the option to search for PDF or PS increases the change of a hit. Also sometimes limiting the search to cs.xyz or xyz.edu increases ... |
[enter link description here][1]As [AJed][2] mentioned, [ACM digital library][3] and [IEEE xplorer][4] would be near the top of list.
Additionally [Goggling with advanced search][5] for the name of the reference with the option to search for PDF or PS increases the change of a hit. Also sometimes limiting the search... |
As [AJed][2] mentioned, [ACM digital library][3] and [IEEE xplorer][4] would be near the top of list.
Additionally [Goggling with advanced search][5] for the name of the reference with the option to search for PDF or PS increases the change of a hit. Also sometimes limiting the search to cs.xyz or xyz.edu increases ... |
null |
Section 2.3.3 in :
[Codd, E.F. (1970). "Relational Completeness of Data Base Sublanguages"][1] is what you need.
[1]: http://classes.soe.ucsc.edu/cmps277/Fall08/Papers/Codd72a.pdf |
null |
null |
Here's something from Slonneger's "Syntax and Semantics of Programming Languages":
> A variable may occur both bound and free in the same lambda
> expression: for example, in λx.yλy.yx the first occurrence of y is
> free and the other two are bound.
I assume the free variable is the y right after the λx. and th... |
Free and Bound in Lambda Calculus |
|lambda-calculus| |
I've added brackets to disambiguate $$\lambda x.(\color{red}y (\color{green}{\lambda y}.(\color{blue}yx)))$$ the red $y$ is free and the blue one is bound by the green abstraction. I don't think it makes sense to say that the green $y$ is bound, but it together with the lambda is a binder.
We can beta reduce the ter... |
null |
I think that the first thing to consider is what is a supported operation?
Does "inserting a value with a specific, fixed key" (e.g. for keys taken from the integer realm, inserting with key = 3) correspond to a supported operation for the min heap?
No, because that operation can be trivially implemented with m... |
The reason that your operation is not listed, is that one is not simply interested in all operations that can be easily implemented using a certain data structure, but rather the other way. Given a set of operations, what is the most efficient way (in terms of space and time) to implement these operations. (But I add m... |
null |
My question: do the non-regular languages have closure properties? For example, if the reverse of L is non-regular, then L is non-regular ? thank you :-) |
Are the non-regular languages closed under reverse, union, concatenation, etc? |
|formal-languages|regular-languages|closure-properties| |
I bought a great puzzle called Icosoku. Wikipedia describes it as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and 12 yellow pins for the corners. The pins are printed with the numbers from 1 to 12, and the triangular tiles have up to... |
Computer program for for solving Icosoku |
|computer-games| |
The Rubik cube is a different beast, but the techniques to study it might come handy. A look at the mathematics (group theory) behind its solution is Joyner's ["Mathematics of the Rubik's Cube"][1], the site http://permutationpuzzles.org with its links might also be of help.
[1]: http://www.permutationpuzzles.org/... |
I've been reading a bit about Hierarchical Temporal Memory and Memory Prediction. I found a great paper: HOW THE BRAIN MIGHT WORK: A HIERARCHICAL AND TEMPORAL MODEL FOR LEARNING
AND RECOGNITION, Dileep George's [dissertation](http://alpha.tmit.bme.hu/speech/docs/education/02_DileepThesis.pdf) for his PhD at Stanford. ... |
null |
Can anyone show how to express complexity class P using first-order logic? (descriptive complexity) |
Expressing complexity class P using first-order logic |
|logic|descriptive-complexity| |
Can anyone show how to express complexity class P using first-order logic with LFP? (descriptive complexity) |
Expressing complexity class P using first-order logic with LFP |
null |
Section 2.3.3 in :
[Codd, E.F. (1972). "Relational Completeness of Data Base Sublanguages"][1] is what you need.
[1]: http://classes.soe.ucsc.edu/cmps277/Fall08/Papers/Codd72a.pdf |
null |
The basic way of implementing state is to explicitly implement the state monad. In fact, if you want a pure interpreter, you will be forced to do so one way or another. Since you have objects, and very likely recursion on those, you probably cannot get away with a stack, you need a heap (beware of memory leaks).
Thu... |
The basic way of implementing state is to explicitly implement the state monad. In fact, if you want a pure interpreter, you will be forced to do so one way or another. Since you have objects, and very likely recursion on those, you probably cannot get away with a stack, you need a heap (beware of memory leaks).
Thu... |
For recognizing hand written letters, you might want to have a look at the [detexify website][1], which is a neat tool for recognizing LaTeX Symbols you write on the screen. On this site, you can also find links to Github with the source code.
[1]: http://detexify.kirelabs.org/classify.html |
null |
At the most basic level, the size of the input is the length of the string that encodes the input given to the Turing Machine - *i.e.* the number of cells it takes up on the tape under the chosen encoding scheme.
In practice though, we often measure the size of the input via proxy measurements. So for problems like ... |
We know that $\text{3-SAT}$ problem is NP-complete, but I am not sure what is meant by size of input. Does this mean number of literals, or number of variables? |
Input size of 3-SAT when analyzing complexity |
|complexity-theory| |
null |
In general, the answer is unknown!, no impossible!.
we conclude the decision version of XOR restriction network flow is NP-Complete.
therefore (it's possible, We can do that) if and only if (P=NP) |
*XOR is not the correct name, but I am looking for some kind of exclusive behavior.*
I am currently solving a set of different (assignment) problems by modeling flow networks and running a min-cost-max-flow algorithm. Flow networks are quite handy because a lot of problems can be reduced to them in an easy and under... |
I am trying to solve a recurrence by using substitution method. The recurrence relation is:
<p>T(n)=4T(n/2)+n<sup>2</sup></p>
My guess is T(n) is Θ(nlogn) (and i am sure about it because of master theorem), and to find an upper bound, i use induction. I tried to show that T(n)<=cn<sup>2</sup>logn but that did not wor... |
Solving T(n)=4T(n/2)+n^2 |
|algorithms|recurrence-relation| |
Lets say I have a global dataset and I run queries over those data set.
For example my dataset would be
* #id, #Name, #Employee, #Birthdate, #number_of_children
* 1, Nick, Nasa, 1982, 1
* 2, Jack, Exon, 1985, 5
* 3, Tom, ABCD, 1978, 0
And I can run queryies on those dataset.
sample queries would be
* #Query... |
Algorithm for query comparison |
|data-sets| |
null |
A SkipList provides the same $O(\log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn't necessary. Since the SkipList is constructed using random coin flips, these bounds only hold as long as the structure of the SkipList is sufficiently "balanced". In particular, with probability $1/n^c... |
Are probabilistic search data structures useful? |
|data-structures|search-trees|probabilistic-algorithms| |
I am trying to solve a recurrence by using substitution method. The recurrence relation is:
$$T(n)=4T(n/2)+n^2$$
My guess is $T(n)$ is $\Theta(n\log n)$ (and I am sure about it because of master theorem), and to find an upper bound, I use induction. I tried to show that $T(n)\le cn^2\log n$ but that did not work, I g... |
Solving $T(n)=4T(n/2)+n^2$ |
null |
I bought a great puzzle called [Icosoku](http://en.wikipedia.org/wiki/Icosoku). Wikipedia describes it as: "The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and 12 yellow pins for the corners. The pins are printed with the numbers from 1 to... |
Speeding up a program solving Icosoku |
That's a recurrence of the form: $T(n)=aT(n/b)+f(n)$. In your case $a=4$, $b=2$, and $f(n)=n^2$. This is case 2 of the master theorem. It follows that $T(n)=\Theta(n^2\log n)$. |
You must subtract a *lower order term* in order to strengthen your inductive hypothesis: try
$T(n) \leq c_1 n^2 \lg n- c_2 n$ and you will be able to show by substitution that $T(n) = O(n^2 \lg n)$ for appropriate values of the constants ($c_2 > 1$ and $c_1$ big enough to correctly handle the initial conditions). |
Another technique that may be suitable for your problem is [backtracking][1]. It is often used for solving puzzles such as 8 queens problem, sudoku, etc.
[1]: http://en.wikipedia.org/wiki/Backtracking |
I am trying to solve a recurrence by using substitution method. The recurrence relation is:
$$T(n)=4T(n/2)+n^2$$
My guess is $T(n)$ is $\Theta(n\log n)$ (and I am sure about it because of master theorem), and to find an upper bound, I use induction. I tried to show that $T(n)\le cn^2\log n$ but that did not work, I g... |
In a comment to [Learning F#: What books using other programming languages can be translated to F# to learn functional concepts?][1] [Makarius][2] stated:
> Note that the "CPS" approach has done great harm to performance in
> SML/NJ. Its physical evaluation model violates too many assumptions
> that are built into... |
The "CPS" approach has done great harm to performance in SML/NJ; reasoning desired |
|functional-programming|proof-assistants| |
I know that master theorem is used for the recurrence relations of the form:
<p>T(n) = aT(n/b) + f(n)</p>
But in my question, i am supposed to solve the following recurrence relation by using master theorem:
<p>T(n) = 2T(n/7) + 5T(n/8) + n</p>
Can i take f(n)=n and since f(n)=Θ(n<sup>log<sub>b</sub>a</sup>), i say ... |
Usage of master theorem for solving recursions |
|recurrence-relation|master-theorem| |
null |
A SkipList provides the same $O(\log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn't necessary. Since the SkipList is constructed using random coin flips, these bounds only hold as long as the structure of the SkipList is sufficiently "balanced". In particular, with probability $1/n^c... |
At first approximation, there is a difference in "locality" of memory access, when a programm just runs forward on the heap in CPS style, instead of the traditional growing and shrinking of stack. Also note that CPS will always need GC to recover your seemingly local data placed on the heap. These observations alone ... |
At first approximation, there is a difference in "locality" of memory access, when a programm just runs forward on the heap in CPS style, instead of the traditional growing and shrinking of stack. Also note that CPS will always need GC to recover your seemingly local data placed on the heap. These observations alone ... |
Well, you can easily get $T(n)=O(n\log n)$, since $2T(n/7)+5T(n/8)\le 7T(n/7)$, and the master theorem gives you that $S(n)=7S(n/7)+n$ is $\theta(n\log n)$.
The question is, can you do better - that is to prove that $T(n)=\theta(n)$. I think that if you follow the proof of the master theorem, you will be able to con... |
Well, you can easily get $T(n)=O(n\log n)$, since $2T(n/7)+5T(n/8)\le 7T(n/7)$, and the master theorem gives you that $S(n)=7S(n/7)+n$ is $\Theta(n\log n)$.
The question is, can you do better - that is to prove that $T(n)=\Theta(n)$. I think that if you follow the proof of the master theorem, you will be able to con... |
You may easily solve this recurrence by using the Akra-Bazzi method, which generalizes the master theorem and allows solving recurrences of the form
$T(n)= \sum\limits_{i = 1}^k {a_i T(n/b_i) + f(n)}$
You need to solve for $p$ the equation
$\sum\limits_{i = 1}^k {a_i b_i^{-p} = 1}$
and the solution to the r... |
You may solve this recurrence by using the Akra-Bazzi method, which generalizes the master theorem and allows solving recurrences of the form
$T(n)= \sum\limits_{i = 1}^k {a_i T(n/b_i) + f(n)}$
You need to solve for $p$ the equation
$\sum\limits_{i = 1}^k {a_i b_i^{-p} = 1}$
and the solution to the recurren... |
Which of the following modes of data transfer is the fastest?
a. DMA
b. Interrupt-based
c. Polling
d. All are equally fast
I do not have the answer, so I cannot check, that's why I am posting here.
I think the answer is D. All are equally fast. In all data transfer cases the speed of data transfer is... |
Fastest data transfer |
|computer-architecture| |
You may solve this recurrence by using the Akra-Bazzi method, which generalizes the master theorem and allows solving recurrences of the form
$T(n)= \sum\limits_{i = 1}^k {a_i T(n/b_i) + f(n)}$
You need to solve for $p$ the equation
$\sum\limits_{i = 1}^k {a_i b_i^{-p} = 1}$
and the solution to the recurren... |
You may solve this recurrence by using the Akra-Bazzi method, which generalizes the master theorem and allows solving recurrences of the form
$T(n)= \sum\limits_{i = 1}^k {a_i T(n/b_i) + f(n)}$
You need to solve for $p$ the equation
$\sum\limits_{i = 1}^k {a_i b_i^{-p} = 1}$
and the solution to the recurren... |
I don't think there is a polynomial probability for losing 'balance'. After you insert an element in a skip list, you build a tower of copies above it by flipping a coin until it comes up heads.
So you have layers with fewer and fewer elements as you reach the top. Since a tower has height $k$ with probability $2^{... |
I don't think there is a polynomial probability for losing 'balance'. After you insert an element in a skip list, you build a tower of copies above it by flipping a coin until it comes up heads.
So you have layers with fewer and fewer elements as you reach the top. Since a tower has height $k$ with probability $2^{... |
Fastest mode of data transfer |
In [Neil Immerman's Descriptive Complexity][1] the proof that P = FO + LFP uses alternating graphs: an alternating graph is a directed graph $G= \{ V, E, A, s, t\}$ where $A$ is the set of nodes marked as universal ($V \setminus A$ are existential). The accessibility relation is defined in this way:
- $P_a^G(x,x)$
... |
There is a variety of systems for Interactive Theorem Proving (ITP) -- see also the conference of that name -- Coq, Isabelle, HOLs, ACL2, PVS etc.
All of them are relatively challenging to learn, and each has its own specific culture. It is like learning a foreign language: lets say you know English already, and th... |
null |
null |
I'm studying for an entrance exam and I have sample questions. One of the questions is this
>Prove that recurrence `T(n) = T(n/5) + T(4n/5)+n/2`
>has a solution `T(n) = omega(n log n)`.
>Solve by drawing the recursion tree.
This is what I drew on my paper:
root: n/2 => (4n/5)/2
... |
solve by drawing the recursion tree? |
|recursion|asymptotics| |
First, "fastest" is an ambiguous term--it can refer to latency or throughput/bandwidth.
Second, DMA is orthogonal to interrupts and polling. I.e., the completion of the DMA can trigger an interrupt or be determined by polling an I/O register (or the memory that is being written in some cases). (Explicit processor ... |
I suggest you to look at other (completely different) approaches, too:
1. write a program that given an Icosoku configuration outputs a SAT instance that can be solved using a [SAT solver][1];
2. (re)write your program using a [constraint programming language][2] (for example [STP][3]) or write a program that give... |
I'm studying for an entrance exam and I have sample questions. One of the questions is this
>Prove that recurrence $T(n) = T(n/5) + T(4n/5)+n/2$
>has a solution $T(n) = omega(n log n)$.
>Solve by drawing the recursion tree.
This is what I drew on my paper:
root: n/2 => (4n/5)/2
... |
null |
I'm studying for an entrance exam and I have sample questions. One of the questions is this
>Prove that recurrence $T(n) = T(n/5) + T(4n/5)+n/2$
>has a solution $T(n) = \omega(n \log n)$.
>Solve by drawing the recursion tree.
This is what I drew on my paper:
root: n/2 => (4n/5)/2
... |
Solve a recurrence by drawing the recursion tree? |
|compilers|functional-programming|proof-assistants|continuations| |
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