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![Split q_1][1]
[1]: https://i.stack.imgur.com/pLc8f.png
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Most of the sortings methods have to move data around in short steps (for example, in merge-short, it makes changes locally, then merges this small piece of data, then merges a bigger one. ..). In consequence, you need many data movements if data is far from its destination.
Quicksort, on the other side tries to int... |
Note: I mean a Push Down automata that can move it's reading head two ways on the input stack.
I recently had the question of determining the computational power of 2 way PDAs in the chomsky hierarchy. I don't entirely understand 2 way PDAs, but I can see how giving the machine just slightly more power of being able... |
How does a 2 way pda work? |
|pushdown-automata| |
Note: I mean a Push Down automata that can move it's reading head two ways on one stack.
I recently had the question of determining the computational power of 2 way PDAs in the chomsky hierarchy. I don't entirely understand 2 way PDAs, but I can see how giving the machine just slightly more power of being able to go... |
null |
Note: I mean a Push Down automata that can move it's reading head two ways on one stack.
I recently had the question of determining the computational power of 2 way PDAs in the chomsky hierarchy. I don't entirely understand 2 way PDAs, but I can see how giving the machine just slightly more power of being able to go... |
Note: I mean a pushdown automaton that can move it's reading head two ways on one stack.
I recently had the question of determining the computational power of two-way PDAs in the Chomsky hierarchy. I don't entirely understand two-way PDAs, but I can see how with slightly more power of being able to go back over its ... |
How does a two-way pushdown automaton work? |
|automata|pushdown-automata| |
Fredman and Saks show in ["The cell probe complexity of dynamic data structures"](http://dl.acm.org/citation.cfm?id=73007.73040) that you cannot do better than $\Theta\left(\frac{\lg m}{\lg \lg m}\right)$ amortized time for the operations you are looking for. They call this problem "list representation".
Dietz prese... |
The [Post Correspondence Problem][1] (PCP) is undecidable.
The *bounded version of the PCP* is $NP$-complete and the *marked version of the PCP* (the words of one of the two lists are required to differ in the first letter) is in $PSPACE$ (1).
**Question 1**: *Are these restricted versions used to prove some comp... |
Restricted versions of the PCP |
|complexity-theory| |
Note: I mean a pushdown automaton that can move it's reading head two ways on one stack.
I recently had the question of determining the computational power of two-way PDAs in the Chomsky hierarchy. I don't entirely understand two-way PDAs, but I can see how with slightly more power of being able to read in two direc... |
believe this is a question at the frontier of knowledge ie basically a research question & from a quick google search, it appears to be mostly open. also for many yrs have believed it to be important and linked to complexity theory lower bounds. you dont mention directly a statistical analysis but that is what is impli... |
The [Post Correspondence Problem][1] (PCP) is undecidable.
The *bounded version of the PCP* is $\mathrm{NP}$-complete and the *marked version of the PCP* (the words of one of the two lists are required to differ in the first letter) is in $\mathrm{PSPACE}$ \[1\].
**Question 1**: *Are these restricted versions use... |
The [Post Correspondence Problem][1] (PCP) is undecidable.
The *bounded version of the PCP* is $\mathrm{NP}$-complete and the *marked version of the PCP* (the words of one of the two lists are required to differ in the first letter) is in $\mathrm{PSPACE}$ \[1\].
1. Are these restricted versions used to prove so... |
Decidable restrictions of the Post Correspondance Problem |
see chaitins research into Omega that shows as I understand it that undecidable problems are [paraphrasing] quite numerous, rampant or dense among statements chosen at random. however you have to be careful how you define U(n), D(n) because they may be actually uncomputable functions. there is also some connections to ... |
Decidable restrictions of the Post Correspondence Problem |
I am not sure if this site is a good site where I can ask questions about wireless networks. Please if it is not a good site and you know good one give it to me so I can you use it in the future.
My question is I want to know how the password that we enter (to connect to a wireless network) encrypts the data on the ... |
How can wireless router password encrypts data using WEP and WPA |
|computer-networks|encryption| |
See Chaitin's research into [Omega](http://en.wikipedia.org/wiki/Chaitin%27s_constant) that shows, as I understand it, that undecidable problems are [paraphrasing] quite numerous, rampant or dense among statements chosen at random. However you have to be careful how you define $U(N)$ and $D(N)$ because they may be actu... |
The $\Theta(\log n)$ complexity is usually connected with subdivision. When using lists as an example, imagine a list whose elements are sorted. You can search in this list in $\mathcal{O}(\log n)$ time - you do not actually need to look at each element because of the sorted nature of the list.
If you look at the e... |
I am not sure if this site is a good site where I can ask questions about wireless networks. Please if it is not a good site and you know good one give it to me so I can you use it in the future.
How does the password that we enter (to connect to a wireless network) encrypt the data on the wireless network?
Throu... |
null |
In terms of (balanced) trees (say, binary tree, so all $\log$'s are base 2):
- $\Theta(1)$ is getting the root of the tree
- $\Theta(\log n)$ is a walk from root to leaf
- $\Theta(n)$ is traversing all nodes of the tree
- $\Theta(n^2)$ is actions on all the subsets two nodes in the tree, e.g., the number of d... |
I am not sure if this site is a good site where I can ask questions about wireless networks. Please if it is not a good site and you know good one give it to me so I can you use it in the future.
How does the password that we enter (to connect to a wireless network) encrypt the data on the wireless network?
Throu... |
|computer-networks|encryption|security| |
A two-way PDA can accept the canonical context-sensitive language $\{0^{n}1^{n}2^{n} | n \geq 1\}$. Such an automaton could work by checking whether the largest prefix of the form $0^{i}1^{j}$ had $i = j$, using the stack, after which it could empty the stack, and check whether the largest suffix of the form $1^{j}2^{k... |
The simplex algorithm walks greedily on the corners of a polytope to find the optimal solution to the linear programming problem. As a result, the answer is always a corner of the polytope. Interior point methods walk the inside of the polytope. As a result, when a whole plane of the polytope is optimal (if the objecti... |
Finding exact corner solutions to linear programming using interior point methods |
|algorithms|optimization| |
How does wireless router password encrypt data using WEP and WPA? |
null |
As explained in [Wikipedia](http://en.wikipedia.org/wiki/Wi-Fi_Protected_Access#Security):
> If ASCII characters are used, the 256 bit key is calculated by applying the PBKDF2 key derivation function to the passphrase, using the SSID as the salt and 4096 iterations of HMAC-SHA1.
For more information see [WPA Key ... |
There is an even simpler definition of invert that works for all countable domains `a`, no exotic execution models needed:
invert(f,y) =
for each x in a:
if f(x) == y: return x
For example if the domain `a` consists of all binary trees, you have to have a method for enumerating binary trees. ... |
There is an even simpler definition of invert that works for all countable domains `a`, no exotic execution models needed:
invert(f,y) =
for each x in a:
if f(x) == y: return x
For example if the domain `a` consists of all binary trees, you have to have a method for enumerating binary trees. ... |
There is an even simpler definition of invert that works for all countable domains `a`, no exotic execution models needed:
invert(f,y) =
for each x in a:
if f(x) == y: return x
For example if the domain `a` consists of all binary trees, you have to have a method for enumerating binary trees. ... |
There is an even simpler definition of invert that works for all countable domains `a`, no exotic execution models needed:
invert(f,y) =
for each x in a:
if f(x) == y: return x
For example if the domain `a` consists of all binary trees, you have to have a method for enumerating binary trees. ... |
|algorithms|optimization|linear-programming| |
*For the lack of detail, this is merely a longer comment:*
[Karmarkar's polynomial time algorithm](https://en.wikipedia.org/wiki/Karmarkar%27s_algorithm) does only move *near* the edge. At the end, it finds a suitable basic solution (e.g. corner) which is optimal using a *purification scheme*¹. You can use this or a... |
SAT stands for the Boolean Satisfiability Problem. |
null |
Turing Completeness + Dataflow Unification = Arbitrarily invertible (pure, nonrecursive) functions? |
While the question in general makes sense, it's odd that you pick maximum matching as an example, because there are many algorithms (max flows for max cardinality bipartite matching, Edmonds' algorithm for nonbipartite matching, and the Hungarian algorithm for max weight bipartite matching) that will all give integer v... |
A family of heuristic search algorithms mimicing the process of natural evolution. |
null |
The Kolmogorov complexity of a string s is equal to the length of the shortest program computing s and halting. Measures the lack of structure in a string. |
null |
Optimization with a linear objective function, subject to linear equality and linear inequality constraints. |
null |
Selecting the best element from some set of available alternatives. |
null |
A piece code capable of self-replicating and spreading from one computer to another. |
null |
An algorithm whose behaviour is determined by its input and a generator producing uniformly random numbers. |
null |
null |
WEP uses the stream cipher $RC4$ for confidentiality and the CRC-32 checksum for integrity. All data frames sent by a router in a WEP protected network are encrypted. When a router sends a packet, the following steps are executed.
1. The router picks a $24$-bit value called the initialization vector $IV$.
A n... |
In coding theory, 'how good code is' means how many channel errors can be corrected, or better put, the maximal noise level that the code can deal with.
In order to get better codes, the codes are designed using a large alphabet (rather than binary one). And then, the code is good if it can deal with a large rate of... |
error-corrting rate is misleading |
|coding-theory| |
Error-correcting rate is misleading |
null |
I came across an issue with the definition of a (directed) graph in Sipser's Introduction to the theory of computation, 2nd Ed.
On pp.10, An **undirected graph**, or simply a **graph**, is a set of points with lines connecting some of the points. The points are called nodes or vertices, and the lines are called edge... |
Is Directed Graph a Graph? |
|graphs| |
The word 'graph' has two meanings: it can be a shorthand for 'undirected graphs' (like how your book defines it) or it can refer to something that is 'graph-like', such as a directed or an undirected graph. The first meaning is most common.
Directed graphs and undirected graphs are not the same thing (arrows versus ... |
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. |
null |
A finite automaton with a stack. |
null |
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