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[Computable analysis][1] studies questions like computability and complexity of real numbers, real functions and operators. A major difference with classical computability theory is that inputs and outputs can be infinite objects (like a real number), whereas in classical computability theory the input and the outputs ... |
null |
computability and complexity in real or complex analysis |
null |
null |
There are numerous containments known. Let $\subseteq$ denote containment and $\subset$ proper containment. Let $\times$ denote incomparability.
Let $LL = \bigcup_k LL(k)$, $LR = \bigcup_k LR(k)$.
##Grammar level##
###For LL###
* $LL(0) \subset LL(1) \subset LL(2) \subset LL(2) \subset \cdots \subset LL(k) ... |
null |
I would like to write a simple program that accepts a set of windows (width+height) and the screen resolution and outputs an arrangement of those windows on the screen such that the windows take the most space. Therefore it is possible to resize a window, while maintaining `output size >= initial size` and the aspect ... |
Search the inter-webs.
[SNAP][1] is a set of networks hosted by a prof at Stanford. Several real world examples in a variety of settings.
[Net Wiki][2] is hosted by a UNC math prof., again several links to real datasets as well as links to other data resources.
[OpenFlights][3] Has airports and routes between... |
_Although your question does not say it, I'm assuming that you do not want windows to overlap._
One approach to this problem is to use a constraint solver such as [Choco][1]. One simply writes down the constraints encoding your problem, tunes the solver to act in a smart way, and then let it run. This means that all... |
I have the following algorithmic problem:
> Determine the space Turing complexity of recognizing DNA strings that are Watson-Crick palindromes. (Watson-Crick palendromes are strings that their reversed complement is the original string. With DNA these are the complements: A is the complement of T. C is the complemen... |
Determining the space complexity of an algorithmic problem |
|space-complexity|turing| |
I have the following algorithmic problem:
> Determine the space Turing complexity of recognizing DNA strings that are Watson-Crick palindromes. (Watson-Crick palendromes are strings that their reversed complement is the original string. With DNA these are the complements: A is the complement of T. C is the complemen... |
To show that a problem has a specific space complexity, one generally needs to come up with an algorithm that has that space complexity. This may require trial and error, but a better approach is to have a good understanding of the problem you are looking at and a good amount of experience in algorithms and complexity.... |
To show that a problem has a specific space complexity, one generally needs to come up with an algorithm that has that space complexity. This may require trial and error, but a better approach is to have a good understanding of the problem you are looking at and a good amount of experience in algorithms and complexity.... |
|turing-machines|space-complexity| |
To show that a problem has a specific space complexity, one generally needs to come up with an algorithm that has that space complexity. This may require trial and error, but a better approach is to have a good understanding of the problem you are looking at and a good amount of experience in algorithms and complexity.... |
I am revising for a computer security course and I am stuck on one of the past questions. Here is it:
![enter image description here][1]
I think I know the first one. Bob needs to take a hash of the received message along with his shared key and compare that hash with the hash received from Alice, if they match t... |
attack on hash function not satisfying one-way property |
|cryptography|computer-security|hash| |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asympototic lower bound does not rule out the possibility that a huge but finite class of problem ins... |
Are asymptotic lower bounds relevant to cryptography? |
|complexity-theory|cryptography|computer-security| |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
>For the second one, would the answer be that an attacker can simply obtain the original message given a hash?
Well, the message $M$ is already given to the adversary, so he need not find it. To break the scheme he needs to send a new pair $M^*, h(..)$ such that Bob will accept $M^*$ as the message sent by Alice.
... |
I am revising for a computer security course and I am stuck on one of the past questions. Here is it:
![enter image description here][1]
I think I know the first one. Bob needs to take a hash of the received message along with his shared key and compare that hash with the hash received from Alice, if they match t... |
|cryptography|hash| |
>For the second one, would the answer be that an attacker can simply obtain the original message given a hash?
Well, the message $M$ is already given to the adversary (it is sent to Bob on an insecure channel), so he needs not find it. To break the scheme he needs to send a new pair $M^*, h(M^*\|S_{ab})$ such that B... |
null |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
I have the following algorithmic problem:
> Determine the space Turing complexity of recognizing DNA strings that are Watson-Crick palindromes.
Watson-Crick palindromes are strings whose reversed complement is the original string. The *complement* is defined letter-wise, inspired by DNA: A is the complement of T... |
The space complexity of recognising Watson-Crick palindromes |
Attack on hash functions that do not satisfy the one-way property |
|algorithms|algorithm-analysis|turing-machines|space-complexity| |
I am revising for a computer security course and I am stuck on one of the past questions. Here is it:
> Alice ($A$) wants to send a short message $M$ to Bob ($B$) using a shared secret $S_{ab}$ to authenticate that the message has come from her. She proposes to send a single message with two pieces:
$$ A \to B: \qu... |
Attack on hash functions that do not satisfy the one-way property |
|algorithms|computational-geometry|packing| |
|algorithms|computational-geometry|packing|user-interface| |
Have a look at splay trees, they are really what you need. You would have to modify the splay function, not to move each accessed node all the way to the tree, but slowly upwards |
I don't quite understand why the rotation in the splay tree data structure is taking into account not only the parent of the rating node, but also the grandparent (zig-zag and zig-zig operation). Why would the following not work:
as we insert, for instance, a new node to the tree, we check whether we insert into the... |
Splay tree rotation algorithm |
|algorithms|binary-trees| |
I don't quite understand why the rotation in the splay tree data structure is taking into account not only the parent of the rating node, but also the grandparent (zig-zag and zig-zig operation). Why would the following not work:
As we insert, for instance, a new node to the tree, we check whether we insert into the... |
|algorithms|binary-trees|spla| |
null |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
The simpler balancing algorithm can require $\Omega(n)$ amortized time per rotation in the worst case. Suppose the tree is just a path of right children. If you access the only leaf in this tree, and rotate it up to the root, you've spent $\Omega(n)$ time, and the resulting tree is just a path of left children. Repe... |
null |
null |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
|algorithms|data-structures|binary-trees|search-trees| |
|algorithms|complexity-theory|binary-trees|algorithm-analysis|search-trees| |
|algorithms|data-structures|binary-trees|search-trees| |
|data-structures|binary-trees|search-trees| |
|data-structures|binary-trees|search-trees| |
null |
null |
An asymptotic lower bound such as exponential-hardness is generally thought to imply that a problem is "inherently difficult". Encryption that is "inherently difficult" to break is thought to be secure.
However, an asymptotic lower bound does not rule out the possibility that a huge but finite class of problem inst... |
[Blache et. al, On Approximation Intractability of the Bandwidth Problem, 1997](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.5794&rep=rep1&type=pdf) confirms there is no PTAS for the problem unless $P = NP$, even for (binary) trees. [Unger W, The Complexity of the Approximation of the Bandwidth Problem, ... |
Suppose we have a set S ={a1,a2,a3,...an} of N coders .
Each Coders has rating Ri and the number of gold medals Ei,they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders,they developed the following strategy.
They first arrange the code... |
Selection Strategy |
|algorithms| |
Suppose we have a set S ={a1,a2,a3,...an} of N coders .
Each Coders has rating Ri and the number of gold medals Ei,they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders,they developed the following strategy.
They first arrange the code... |
Suppose we have a set $S = \{ a_1,a_2,a_3,\ldots , a_N \}$ of $N$ coders .
Each Coders has rating $R_i$ and the number of gold medals $E_i$,they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders,they developed the following strategy:
Th... |
Selecting the 3 middle items of an array in less than $O(n\log n)$ time. |
null |
This is a problem of selecting the $k$th smallest element from the list solved by a class of algorithms called the [Selection Algorithms][1]. There exist deterministic linear time selection algorithms so your problem can be solved in linear time by selecting the $n/2,n/2-1,n/2+1$ elements from the original unsorted lis... |
This is a problem of selecting the $k$th smallest element from the list solved by a class of algorithms called the [Selection Algorithms][1]. There exist deterministic linear time selection algorithms so your problem can be solved in linear time by selecting the $n/2,n/2-1,n/2+1$th smallest elements from the original u... |
Recently I found in a paper ("Finding a shortest solution for the NxN extension of the 15-Puzzle is intractable") a special symmetric version of SAT called the **2/2/4-SAT**. But there are many variants out there, for example **MONOTONE NAE-3SAT**, **MONOTONE 1-IN-3-SAT**, ...
Are there survey papers (or web pages) ... |
List of intractable/tractable SAT variants |
|satisfiability| |
Suppose we have a set $S = \{ a_1,a_2,a_3,\ldots , a_N \}$ of $N$ coders .
Each Coders has rating $R_i$ and the number of gold medals $E_i$,they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders,they developed the following strategy:
Th... |
Selecting the 3 middle items of an array in $o(n\log n)$ time |
Recently I found in a paper ("Finding a shortest solution for the NxN extension of the 15-Puzzle is intractable") a special symmetric version of SAT called the **2/2/4-SAT**. But there are many NP-complete variants out there, for example: **MONOTONE NAE-3SAT**, **MONOTONE 1-IN-3-SAT**, ...
Some other variants are tr... |
List of intractable/tractable satisfiability problem variants |
**Planar-3SAT** meaning the planar version of **3SAT** is known to be **NP**-complete. See [D Lichtenstein, Planar formulae and their uses, 1981](http://link.aip.org/link/?SMJCAT/11/329/1).
Not-All-Equal 3SAT (**NAE-3SAT**) is **NP**-complete. However, the planar version of it is in **P** as shown by [Moret, Planar ... |
As mentioned by Standa Zivny on the related question of CSTheory, [Which SAT problems are easy?](http://cstheory.stackexchange.com/questions/4375/which-sat-problems-are-easy), there's a well-known result by [Schaefer from 1978](http://dx.doi.org/10.1145/800133.804350) (quoting the answer of Zivny):
> If SAT is param... |
null |
The simpler balancing algorithm can require $\Omega(n)$ amortized time per rotation in the worst case. Suppose the tree is just a totally unbalanced path of right children; no node has a left child. The only leaf in this tree is the tree with the maximum key. If you rotate this step by step up to the root, you've us... |
The simpler balancing algorithm can require $\Omega(n)$ amortized time per rotation in the worst case. Suppose the tree is just a totally unbalanced path of right children; no node has a left child. The only leaf in this tree is the tree with the maximum key. If you rotate this step by step up to the root, you've us... |
Recently I found in a paper ("Finding a shortest solution for the NxN extension of the 15-Puzzle is intractable") a special symmetric version of SAT called the **2/2/4-SAT**. But there are many NP-complete variants out there, for example: **MONOTONE NAE-3SAT**, **MONOTONE 1-IN-3-SAT**, ...
Some other variants are tr... |
Classification of intractable/tractable satisfiability problem variants |
Let's say that we have a large collection of tasks $\tau_1, \tau_2, ..., \tau_n$ and a collection of identical (in terms of performance) processors $\rho_1, \rho_2, ..., \rho_m$ which operate completely in parallel. For scenarios of interest, we may assume $m \leq n$. Each $\tau_i$ takes some amount of time/cycles to c... |
How does variance in task completion time affect makespan? |
|probability-theory|scheduling|parallel-computing| |
|complexity-theory|satisfiability| |
null |
Often I see a sentence like this while reading texts on Computational Complexity:
"For this special case of TSP" or
"This is a special case of SAT" or
"k-PARTITION is the following special case of BIN PACKING" or
"SUBSET SUM is a special case of KNAPSACK" ad nauseam.
What I find missing is the criter... |
Special Case Complexity |
|complexity-theory| |
#Classic, well-known results#
As mentioned by Standa Zivny on the related question of CSTheory, [Which SAT problems are easy?](http://cstheory.stackexchange.com/questions/4375/which-sat-problems-are-easy), there's a well-known result by [Schaefer from 1978](http://dx.doi.org/10.1145/800133.804350) (quoting the answe... |
When we say that a problem $B$ is a special case of a problem $A$, we mean that $B$ is the same problem as $A$, with the exception that not all problem instances of $A$ are problem instances for $B$. If $B$ is a special case of $A$, we say that $A$ is a generalization of $B$.
Two examples: the addition of positive w... |
Often I see a sentence like this while reading texts on Computational Complexity:
"For this special case of $\text{TSP}$" or
"This is a special case of $\text{SAT}$" or
"$k$-$\text{PARTITION}$ is the following special case of $\text{BIN PACKING}$" or
"$\text{SUBSET SUM}$ is a special case of $\text{KNAPSA... |
Complexity of Special Case Problems |
Recently I found in a paper ("*Finding a shortest solution for the $N$x$N$ extension of the 15-Puzzle is intractable*") a special symmetric version of SAT called the **2/2/4-SAT**. But there are many $\text{NP}$-complete variants out there, for example: **MONOTONE NAE-3SAT**, **MONOTONE 1-IN-3-SAT**, ...
Some other ... |
|complexity-theory|reference-request|satisfiability| |
Suppose we have a set $S = \{ a_1,a_2,a_3,\ldots , a_N \}$ of $N$ coders.
Each Coders has rating $R_i$ and the number of gold medals $E_i$, they had won so far.
A Software Company wants to hire exactly three coders to develop an application.
For hiring three coders, they developed the following strategy:
... |
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