instruction stringlengths 0 29.8k ⌀ |
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"The access patterns of user requests may be **static**, so that they do
not change over time, or dynamic. It is obviously considerably easier to plan for
and manage the **static** environments than would be the case for dynamic distributed
systems. Unfortunately, it is difficult to find many real-life distributed a... |
Static access pattern in Distributed Databases |
|distributed-systems|databases| |
This problem is as hard as comparison sorting, given `n` input number sort them.
You can make interval set from input number set $S$ (w.l.o.g suppose input numbers are in $Z^+$) as follow:
$ \Gamma = \{(a,b) \mid a\in S \wedge b=\max_{t\in S} \{2\cdot t - a + 1 \} \}$
Above transformation can be done in $O(n)$... |
First your integer numbers are converted into binary numbers. For example, in CPU integer 2 is converted to 0010. Then, from [Digital comparator on Wikipedia:](http://en.wikipedia.org/wiki/Digital_comparator)
> A `digital comparator` or magnitude comparator is a hardware electronic
> device that takes two numbers as ... |
I found what you copied in the following [text][1]
The idea is that users access (querying, updating or etc ..) of the database changes with time. It may be at its peaks in sale seasons for example if the database belongs to a commercial applications. etc ..
From your copied text: it says that: "it is difficult ... |
Difference between reductions in algebraic problems versus reductions in computational intractability |
Using this grammar, over the alphabet {a}
prod 1: S -> a
prod 2: S -> CD
prod 3: C -> ACB
prod 4: C -> AB
prod 5: AB -> aBA
prod 6: Aa -> aA
prod 7: Ba -> aB
prod 8: AD -> Da
prod 9: BD -> Ea
prod 10: BE ->Ea
prod 11: E -> a
Im trying to show that the workin... |
Generate the word using this grammar |
|formal-grammars| |
When I read about NP-completeness for the first time, I really wondered why is the concept of reductions given such high emphasis, after all we have been looking at concepts such as reductions and 'special case of one another problem' in mathematics since elementary algebra. What I mean by reductions in algebra is the ... |
I found what you copied in the following [text][1]
The idea is that users access (querying, updating or etc ..) of the database changes with time. It may be at its peaks in sale seasons for example if the database belongs to a commercial applications. etc .. - if it is always fixed and predicted then it is static.
... |
First your integer numbers are converted into binary numbers. For example, in CPU integer 2 is converted to 0010.
> A `digital comparator` or magnitude comparator is a hardware electronic
> device that takes two numbers as input in binary form and determines
> whether one number is greater than or less than or equa... |
Start at the end! Only one applicable production: #8. $D$ moves backward over the $A$'s turning them into $a$'s. Then use #9, and repeatedly #10.
Please take a piece of paper, and count the $a$'s generated. Probably the expression ${n+1}^2 = n^2+2n+1$ is useful. |
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 ... |
I need to know what class of CFL is closed under i.e. what set is complement of CFL.
I know CFL is not closed under complement, and I know that P is closed under complement. Since CFL $\subsetneq$ P I can say that complement of CFL is included in P(right?). There is still a question whether complement of CFL is proper... |
What is complement of Context-free languages? |
|context-free|closure-properties|sets| |
null |
[Binet's formula](http://en.wikipedia.org/wiki/Fibonacci_number) for the nth Fibonacci numbers is remarkable because the equation "converts" via a few arithmetic operations an irrational number $\phi$ into an integer sequence. however, using finite precision arithmetic, one would always have some (small) roundoff error... |
calculating Binet's formula for Fibonacci numbers with arbitrary precision |
|algorithms|discrete-mathematics|floating-point|arithmetic|mathematical-programming| |
One can understand your question in two ways, according to the definition of "the complement of CFG".
**case A:** Complement of CFG is the class of all the languages that are not in CFG.
In that case, the complement is way bigger than $P$, it even has languages that are not in $R$..
But maybe that's not what you... |
One can understand your question in two ways, according to the definition of "the complement of CFL".
**case A:** Complement of CFL is the class of all the languages that are not in CFL.
In that case, the complement is way bigger than $P$, it even has languages that are not in $R$..
But maybe that's not what you... |
|algorithms|algorithm-analysis|correctness-proof|loop-invariants| |
null |
[Binet's formula](http://en.wikipedia.org/wiki/Fibonacci_number) for the nth Fibonacci numbers is remarkable because the equation "converts" via a few arithmetic operations an irrational number $\phi$ into an integer sequence. However, using finite precision arithmetic, one would always have some (small) roundoff error... |
Calculating Binet's formula for Fibonacci numbers with arbitrary precision |
Yes, this is called the *Product Constuction* - given DFAs $M_1$ and $M_2$, we can construct $M=M_1\times M_2$:
- $M$ consists of pairs of states from its constituent DFAs, so if the original DFAs
have states $A,B,C$ and $x,y,z$, the product would be $\{Ax,Ay,Az,Bx,By,Bz,Cx,Cy,Cz\}$.
- The transition functio... |
null |
A very large fraction of new computer science papers come up on arxiv: http://arxiv.org/corr/home.
If you are interested in complexity theory give ECCC a look: http://eccc.hpi-web.de/.
If you are interested in crypto, there is the IACR eprint archive: http://eprint.iacr.org/.
All of these are free and frankly... |
null |
It's a design choice for the cache. So if you are designing a cache, do both and examine the consequence in term of performance, complexity of the design and other impacts in order to make your choice.
If you are trying predicting for a given cache, look at its spec.
And note anyway that cache have often a more ... |
Start at the end! There is only one applicable production: #8. $D$ moves backward over the $A$'s turning them into $a$'s. Then use #9, and repeatedly #10.
Please take a piece of paper and count the $a$'s generated. Probably the expression $(n+1)^2 = n^2+2n+1$ is useful. |
null |
In the other answers good sources are given. What I like to add is that not only you should try to locate single papers in a field, but also to find in what conferences they have been published. Then you can take some volumes of recent years and browse a little what has been happening there. Conference series might be ... |
As the comments show, roundig is a respected method for Fibonacci computations. See also "Computation by rounding" in the wiki-lemma.
You avoid roundoff by computing exactly, but using numbers of the form $a+b\sqrt5$: $(a+b\sqrt5)(c+d\sqrt5) = (ac+5bd)+(bd+ac)\sqrt5$. Technically that is $Z[\sqrt5]$ I believe. But I... |
I think, that the part `with some other useless information...` in your problem specification must contain some information on solving your problem. As I was trying to calculate the numbers that you got I found some errors, and I thought there must be some more input. Let me first explain:
Your formulas are incorrec... |
I think, that the part `with some other useless information...` in your problem specification must contain some information on solving your problem. As I was trying to calculate the numbers that you got I found some errors, and I thought there must be some more input. Let me first explain:
Your formulas are incorrec... |
As the comments show, roundig is a respected method for Fibonacci computations. See also "Computation by rounding" in the wiki-lemma.
You avoid roundoff by computing exactly, but using numbers of the form $a+b\sqrt5$: $(a+b\sqrt5)(c+d\sqrt5) = (ac+5bd)+(ad+bc)\sqrt5$. Technically that is $Z[\sqrt5]$ I believe. But I... |
This problem is as hard as comparison sorting, given `n` input number sort them.
You can make interval set from input number set $S$ (w.l.o.g suppose input numbers are in $Z^+$) as follow:
$ \Gamma = \{(a,b) \mid a\in S \wedge b=\max_{t\in S} \{2\cdot t - a + 1 \} \}$
Above transformation can be done in $O(n)$... |
I was solving the following problem. But I am not able to think an efficient algorithm for this modified version of problem.The Problem Statement is :
We are given **K Rectangles**. The Dimensions of xth Rectangle is (Nx * Mx),where 1<=x<=K.
From each rectangle x , Alice Cuts a rect. of dimension (Px*Qx),where 1<... |
Modified paths Counting in a Rectangle |
|algorithms| |
I was solving the following problem. But I am not able to think an efficient algorithm for this modified version of problem.The Problem Statement is :
We are given **K Rectangles**. The Dimensions of xth Rectangle is (Nx * Mx),where 1<=x<=K.
From each rectangle x , Alice Cuts a rect. of dimension (Px*Qx),where 1<... |
I was solving the following problem. But I am not able to think of an efficient algorithm for this modified version of problem. The problem statement is:
> We are given **K Rectangles**. The dimensions of xth Rectangle is (Nx * Mx),where 1<=x<=K.
From each rectangle x , Alice Cuts a rect. of dimension (Px*Qx),wher... |
I think this questions exploits only a technicality. However, you can follow this path
1. The class of ${\sf P}$-complete languages does not contain $\Sigma^*$ and $\emptyset$. This is true for all classes and not only ${\sf P}$, since in order to reduce a language $L_1\neq\emptyset,\Sigma^*$ to another language $L_... |
Provided that we have to compare it against the graph coloring problem which is NPC. So far,
I can only think of connecting edges from a vertex in a provided graph to all the other edges it is not connected to then I separate the new graph g2, then I connect all the vertices that are not connected in the g2. And then ... |
Proving that clique cover problem is NP complete |
|np-complete| |
I am really confused about clique problem and clique cover problem. I tried googling it,but I don't see to be able to visualise the clique cover problem. Thanks |
What exactly is a clique cover problem |
|np-complete|clique| |
null |
you can find answer of these in title itself.
> `image processing`- title says that it processes image, means does
> some transformations on image. that means may be it does some
> smoothing,sharpening, contrasting,stretching.. on the image for making
> image more enhancive & readable that is input and output of... |
A clique is a simple undirected graph with all of the possible edges. It is also known as a complete graph, but clique is more often used to referring to subgraphs that are complete graphs.
The clique cover problem asks whether a graph's vertices can be partitioned into $k$ or fewer sets such that each set of vertic... |
|graphs|np-complete|reductions| |
As mentioned in the comments, DP is a perfectly valid solution to the problem. If the numbers are too large to calculate directly the number of solutions, then you can take things mod 10^9 + 7 during intermediate steps, too. This will work out because $(a \% b + c \% b) \% b = (a + c) \% b$ (for positive numbers or pro... |
|algorithms|combinatorics|dynamic-programming| |
First your integer numbers are converted into binary numbers. <br/>For example, in CPU integer 2 is converted to 0010.
> A `digital comparator` or magnitude comparator is a hardware electronic
> device that takes two numbers as input in binary form and determines
> whether one number is greater than or less than or... |
null |
|complexity-theory|formal-languages|context-free|closure-properties|sets| |
Coming from the POV of someone who has just started his MS in CS program, but is seriously considering eventually going into for his PhD.
I am having trouble deciding what I will focus my research on when I go for my PhD (though I definitely know I want to go for my PhD). See [also this question on academia.SE](http... |
Where to find published research papers? |
I am really confused about clique problem and clique cover problem. I tried googling it,but I don't see to be able to visualise the clique cover problem. |
What exactly is a clique cover problem? |
|complexity-theory|terminology|np-complete| |
I am learning about software design patterns by reading Wikipedia pages about them. A lot of the patterns such as the bridge pattern have diagrams with boxes and different kinds of arrows:
[![enter image description here][1]](https://i.stack.imgur.com/ZPF7S.png)
<sup>Source: [Wikipedia](http://upload.wikimedia.or... |
|terminology|software-engineering| |
ConcreteImplementer inherits from Implementer,
Same for RefinedAbstraction and Abstraction
The other arrow: these classes composes without belonging to each other.
See also [here](http://www.ivencia.com/softwarearchitect/chapter1/chapter1_6.htm).
The paper-like box is a note (a comment). |
> **Possible Duplicate:**
> [Proof of linear search?](http://cs.stackexchange.com/questions/6597/proof-of-linear-search)
<!-- End of automatically inserted text -->
I'm reading the MIT Press, Introduction to Algorithms textbook 3rd edition, and I am a bit confused by an exercise.
2.1-3
Consider the searching... |
{"OriginalQuestionIds":[6597],"Voters":[{"Id":472,"DisplayName":"Juho"},{"Id":1636,"DisplayName":"Luke Mathieson"},{"Id":98,"DisplayName":"Raphael"}]} |
A very large fraction of new computer science papers come up on arxiv: http://arxiv.org/corr/home.
If you are interested in complexity theory give ECCC a look: http://eccc.hpi-web.de/.
If you are interested in crypto, there is the IACR eprint archive: http://eprint.iacr.org/.
All of these are free and frankly... |
Assume a map-reduce program has $m$ mappers and $n$ reducers ($m > n$). The output of each mapper is partitioned according to the key value and all records having the same key value go into the same partition (within each mapper), and then each partition is sent to a reducer. Thus there might be a case in which there a... |
How partitioning in map-reduce work? |
|distributed-systems|parallel-computing|algorithm-design| |
**Question 1:** What is the average access time for a 3-level memory system with access time $T_1$, $2T_1$ and $3T_1$? (Hit ratio $h_1$ = $h_2$ = 0.9)
The solution given is: $0.9[T_1] + 0.1(0.9[2*T_1] + 0.1[3*T_1]) = 1.11[T_1]$ **(Method 1)**
Here, they have considered the page won't be copied to the lower level... |
I was solving the following problem. But I am not able to think of an efficient algorithm for this modified version of problem. The problem statement is:
> We are given **K Rectangles**. The dimensions of $x$-th Rectangle is ($N_x \times M_x$), where $1\leq x \leq K$.
From each rectangle $x$ , Alice Cuts a rect. o... |
**Question 1:** What is the average access time for a 3-level memory system with access time $T_1$, $2T_1$ and $3T_1$? (Hit ratio $h_1$ = $h_2$ = 0.9)
The solution given is: $0.9[T_1] + 0.1(0.9[2*T_1] + 0.1[3*T_1]) = 1.11[T_1]$ **(Method 1)**
Here, they have considered the page won't be copied to the lower level... |
I know that a [one-way function][1] is informally a function that it's easy to compute but hard to invert.<br/>
If f(x) is a one way function the function $g(x) = x\oplus f(x)$ is a one-way function?
My intuition is that it's but i not really sure.
[1]: http://en.wikipedia.org/wiki/One-way_function |
What will i obtain if i apply a xoring a one way function and it's input? |
|complexity-theory|cryptography| |
Let's take a simple example, Counting word into a distributed set of documents:
each mapper takes in input a list of document, and returns a list of pairs word and how many times this word occurs. There is an intermediate layer that takes the outputs of all the mapper and groups values by key. After that the reducer... |
What will i obtain if i apply a xor-ing a one way function and it's input? |
Let's take a simple example, Counting word into a distributed set of documents:
each mapper takes in input a list of document, and returns a list of pairs word and how many times this word occurs. There is an intermediate layer that takes the outputs of all the mapper and groups values by key. After that the reducer... |
null |
If we limit a turing machine so that it is not allowed to write the symbol that it reads would it reduce its power?
For example: $( State, A, State, Z, DIRECTION)$
A cannot be the same symbol as Z.
Cheers
|
Would this limit the power of a turing machine |
|turing-machines| |
Let $h$ be any one-way function, and define $f(x) = 0^{|x|} h(x)$. Note that $f$ is also one-way: it is easy to compute, and if you can invert $f$ you can invert $h$ (so since $h$ is hard to invert, so is $f$). But $g(x) = xh(x)$ is easy to invert. |
If you give me a standard Turing Machine, I can build a must-write-different Turing Machine that does the same thing.
I'll take the original alphabet and double it -- so for symbol $a$, I create two symbols $a_1$ and $a_2$, and for symbol $b$, I create $b_1$ and $b_2$.
Now I treat both $a_1$ and $a_2$ in the exac... |
|formal-grammars|context-free| |
> The access patterns of user requests may be **static**, so that they do
not change over time, or dynamic. It is obviously considerably easier to plan for
and manage the **static** environments than would be the case for dynamic distributed
systems. Unfortunately, it is difficult to find many real-life distributed ... |
If you give me a standard Turing Machine, I can build a must-write-different Turing Machine that does the same thing.
I'll take the original alphabet and double it -- so for symbol $a$, I create two symbols $a_1$ and $a_2$, and for symbol $b$, I create $b_1$ and $b_2$.
Now I treat both $a_1$ and $a_2$ in the exac... |
|computability|turing-machines|machine-models| |
If we limit a turing machine so that it is not allowed to write the symbol that it reads would it reduce its power?
For example: $( State, A, State, Z, DIRECTION)$
$A$ cannot be the same symbol as $Z$.
|
Does forcing TMs to change all symbols they read change their power? |
If you want to know about how an actual CPU does it, it's something like this.
A CPU operates on numbers of only up to a certain size. Nowadays that's usually 64-bit integers (we'll ignore floating-point numbers; the idea will be similar).
So we should recognize that
1. A CPU is storing numbers up to (say) 64 ... |
null |
One can understand your question in two ways, according to the definition of "the complement of CFL".
**case A:** Complement of CFL is the class of all the languages that are not in CFL. Formally, $$\overline{CFL} = \{ L \mid L\notin CFL\}.$$
In that case, $\overline{CFL}$ is way bigger than $P$, it even has langu... |
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