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|asymptotics|landau-notation|mathematical-analysis| |
|lambda-calculus|quantum-computing|reference-request|computation-models| |
|complexity-theory|efficiency|computation-models| |
|quantum-computing|turing-machines|computation-models| |
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Another way to think about it more intuitively, is to see that the main thing you have to show is that $(\log_3(n))^5$ is $O(n^{0.2})$, or equivalently that $\log_3(n)$ is $O(n^{0.04})$. Logs always grow slower than any constant power of n, no matter how small.
If you want to formalize the last sentence, then you c... |
I am slightly confused by some terminology I have encountered regarding the complexity of optimization problems. In an algorithms class, I had the [large parsimony](http://en.wikipedia.org/wiki/Maximum_parsimony_%28phylogenetics%29#Problems_with_maximum_parsimony_phylogeny_estimation) problem described as NP-complete.... |
"NP-complete" optimization problems |
|np-complete| |
|compilers|parsers| |
|complexity-theory|np-complete| |
A method in analysis of algorithms that considers the overall cost of a sequence of operations. |
null |
[Asymptotic analysis][1] is a method of describing the limiting behavior. It is has application in computer science, particularly in analyzing the asymptotic behavior of algorithms and computational processes.
Related tags:
* [tag:landau-notation]
[1]: http://en.wikipedia.org/wiki/Asymptotic_analysis |
null |
Questions about the asymptotic notations and analysis |
null |
Heuristics are often faster than exact methods, but usually only provide approximations. |
null |
[Mathematical analysis][1] is a branch of mathematics.
[1]: http://en.wikipedia.org/wiki/Mathematical_analysis |
null |
Questions related to mathematical analysis (often called analysis by mathematicians) |
null |
the definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems. |
null |
The hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.
NP complete problems have two properties:
1. They are in the [NP complexity class](https://en.wikipedia.org/wiki/NP_%28complexity%29) (can be solved by nondeterministic Turing-machine)
2. They ... |
null |
A theoretical model of mechanical computation capable of simulating any computer program. |
null |
A tree data structure with each internal node having exactly eight children. |
null |
I am trying to compare the performance of a classification result with Bayes classifier, K-NN, Piece wise component analysis (PCA). I have doubts regarding the following (please excuse my lack of programming skills since I am a biologist and not a programmer thus finding hard to follow the matlab documentation)
... |
Pattern classification issues and plots |
|machine-learning|pattern-recognition| |
There are a bunch of cool recursive algorithms [1], [2] used in RNA & protein secondary structure prediction. Left to its own devices, a strand of RNA will form base pairs with itself.
One relatively simple example from [3] computes the maximum number of nested, paired bases an RNA string will form with itself:
... |
There are a bunch of cool recursive algorithms [1], [2] used in RNA secondary structure prediction. Left to its own devices, a strand of RNA will form base pairs with itself; one relatively simple example from [3] computes the maximum number of nested, paired bases an RNA string will form with itself:
$M(i,j)=\unde... |
I am trying to compare the performance of a classification result with Bayes classifier, K-NN, Piece wise component analysis (PCA). I have doubts regarding the following (please excuse my lack of programming skills since I am a biologist and not a programmer thus finding the matlab documentation hard to follow )
... |
null |
Consider a CSP model where changing the value of a particular variable is expensive. Is there any work where the objective function also considers the number of changes in the value of the variable during the search process?
PS: Somebody please create a constraint-programming tag for this question (currently I am no... |
In Constraint Programming, is that any model that takes into account the number of variable changes? |
|searching| |
the definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems. |
null |
The definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems. |
null |
In Constraint Programming, are there any models that take into account the number of variable changes? |
|constraint-programming| |
Consider a CSP model where changing the value of a particular variable is expensive. Is there any work where the objective function also considers the number of changes in the value of the variable during the search process? |
null |
I am trying to compare the performance of a classification result with Bayes classifier, K-NN, Piece wise component analysis (PCA). I have doubts regarding the following (please excuse my lack of programming skills since I am a biologist and not a programmer thus finding the Matlab documentation hard to follow).
In ... |
Pattern classification: what goes into the sample? |
There are a bunch of cool recursive algorithms [1], [2] used in RNA secondary structure prediction. Left to its own devices, a strand of RNA will form base pairs with itself; one relatively simple example from [3] computes the maximum number of nested, paired bases an RNA string will form with itself:
$M(i,j)=\unde... |
Because you are using an array, it costs $O(n)$ to insert an item - when you add something to the middle of an array, for example, you have to shift all of the elements after it by one so that the array remains sorted.
The fastest way to find out where to put the item is like you mentioned, a binary search, which is... |
null |
null |
[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 trees. [Unger W, The Complexity of the Approximation of the Bandwidth Problem, 1998](htt... |
Consider a CSP model where changing the value of a particular variable is expensive. Is there any work where the objective function also considers the number of changes in the value of the variable during the search process?
Update: An example: The expensive-to-change variable may be in the control of some other age... |
Minimum bandwidth problem is to a find an ordering of graph nodes on integer line that minimizes the largest distance between any two adjacent nodes.
The decision problem is NP-complete even for binary trees. [Complexity Results for Bandwidth Minimization. Garey, Graham, Johnson and Knuth, SIAM J. Appl. Math., Vol.... |
Approximation of minimum bandwidth on binary trees |
|complexity-theory|np-complete|reference-request|approximation| |
null |
An attempt on a partial answer:
*Decision problems* where already investigated for some time before *optimization problems* came into view, in the sense as they are treated from the approximation algorithms prespective.
So you have to be careful when carrying over the concepts from decision problems. It can be do... |
An attempt on a partial answer:
*Decision problems* where already investigated for some time before *optimization problems* came into view, in the sense as they are treated from the approximation algorithms prespective.
So you have to be careful when carrying over the concepts from decision problems. It can be do... |
null |
Does there exist a set of computations that need to be performable in a programming language in order for it to be considered Turing Complete?
From what I can tell from [wikipedia][1], the language needs to support recursion, or, seemingly, must be able to run without halting. Is this all there is to it?
[1]:... |
Are there minimum criteria for Turing completeness |
|turing-machines| |
An attempt on a partial answer:
*Decision problems* where already investigated for some time before *optimization problems* came into view, in the sense as they are treated from the approximation algorithms prespective.
So you have to be careful when carrying over the concepts from decision problems. It can be do... |
> Does there exist a set of computations that need to be performable in a programming language in order for it to be considered Turing Complete?
Yes, in order to be considered Turing complete a programming language needs to be able to perform any computation that can be performed by a Turing machine. So as a minimum... |
> Does there exist a set of computations that need to be performable in a programming language in order for it to be considered Turing Complete?
Yes, in order to be considered Turing complete a programming language needs to be able to perform any computation that can be performed by a Turing machine. So as a minimum... |
This isn't a general answer to your question, but by the [structured programming theorem][1], all that is needed is the ability to do selection (e.g., `if` in C/C++) and repetition (e.g., `while` in C/C++).
Since both of these can be implemented using a conditional jump instruction (e.g., `JNZ` in x86), that is also... |
This isn't a general answer to your question, but by the [structured programming theorem][1], all that is needed is the ability to do selection (e.g., `if` in C/C++) and repetition (e.g., `while` in C/C++).
Since both of these can be implemented using a conditional jump instruction (e.g., `JNZ` in x86), that is also... |
This isn't a general answer to your question, but by the [structured programming theorem][1], all that is needed is the ability to do selection (e.g., `if` in C/C++) and repetition (e.g., `while` in C/C++). *Edit: as pointed out by Dave Clark in the comments, the structured programming theorem also requires sequence. I... |
This isn't a general answer to your question, but by the [structured programming theorem][1], all that is needed is the ability to do selection (e.g., `if` in C/C++) and repetition (e.g., `while` in C/C++). *Edit: as pointed out by Dave Clark in the comments, the structured programming theorem also requires sequence. I... |
This isn't a general answer to your question, but by the [structured programming theorem][1], all that is needed is the ability to do selection (e.g., `if` in C/C++) and repetition (e.g., `while` in C/C++). *Edit: as pointed out by Dave Clarke in the comments, the structured programming theorem also requires sequence. ... |
The set difference operator (e.g., `EXCEPT` in some SQL variants) is one of the many fundamental operators of relational algebra. However, there are some databases that do not support the set difference operator directly, but which support `LEFT JOIN` (a kind of outer join), and in practice this can be used instead of ... |
Note that by "two-way pushdown automaton", I mean a pushdown automaton that can move its reading head both ways on the input tape.
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 the ability ... |
This a homework question from Udi Manber's book. Any hint would be nice :)
I must show that:
>$n(\log_3(n))^5 = O(n^{1.2})$
I tried using Theorem 3.1 of book:
>$f(n)^c = O(a^{f(n)})$ (for $c > 0$, $a > 1$)
Substituing:
$(\log_3(n))^5 = O(3^{\log_3(n)}) = O(n) $
but $n(log_3(n))^5 = O(n\cdot n) = O(... |
null |
I always though that [$\mu$-recursive functions](https://en.wikipedia.org/wiki/%CE%9C-recursive_function) nailed it. Here is what defines the whole set of computable functions; it is the smallest set of functions containing resp. closed against:
1. The constant $0$ function
2. The successor function
3. Selectin... |
This is cross-posted from [SO](http://stackoverflow.com/questions/4149840/about-codds-reduction-algorithm). I'll also copy the question verbatim from there:
[Codd's Algorithm][1] converts an expression in tuple relational calculus to Relational Algebra. I'd like to know:
1. whether there's a standard implementat... |
About Codd's reduction algorithm |
|database-theory| |
I always though that [$\mu$-recursive functions](https://en.wikipedia.org/wiki/%CE%9C-recursive_function) nailed it. Here is what defines the whole set of computable functions; it is the smallest set of functions containing resp. closed against:
1. The constant $0$ function
2. The successor function
3. Selectin... |
There is a general historical trend.
In the olden days, memories were small, and so programs were perforce small. Also, compilers were not very smart, and many programs were written in assembler, so it was considered a good thing to be able to write a program using few instructions. Instruction pipelines were simple... |
This is cross-posted from [SO](http://stackoverflow.com/questions/4149840/about-codds-reduction-algorithm) over a year ago, but didn't receive a good answer. I'll also copy the question verbatim from there:
[Codd's Algorithm][1] converts an expression in tuple relational calculus to Relational Algebra. I'd like to k... |
null |
The x86 instruction set is a bit of a special case. I think that Motorola's 68K and DEC's VAX are somewhat better examples of CISC. In the days of a lot of assembly-language code, people thought that a very regular, very inclusive ISA was better: I believe they called the difference between assembly code and the way p... |
_This was posted on [SO](http://stackoverflow.com/questions/4149840/about-codds-reduction-algorithm) over a year ago, but it didn't receive a good answer._
[Codd's Algorithm][1] converts an expression in tuple relational calculus to Relational Algebra. I'd like to know:
1. whether there's a standard implementat... |
[Codd's Algorithm][1] converts an expression in tuple relational calculus to Relational Algebra.
1. Is there a standard implementation of the algorithm?
2. Is this algorithm used anywhere? (It seems that the industry only needs SQL and variants, I'm not sure about database theorists in academia.)
3. What's the... |
I am looking for an efficient algorithm that lets me process the minimax search tree for chess with alpha-beta pruning on a distributed architecture. The algorithms I have found (PVS, YBWC, DTS) are all quite old (1990 being the latest). I assume there have been many substantial advancements since then. What is the cur... |
distributed alpha beta pruning |
|distributed-systems|search-problem| |
I am looking for an efficient algorithm that lets me process the minimax search tree for chess with alpha-beta pruning on a distributed architecture. The algorithms I have found (PVS, YBWC, DTS see below) are all quite old (1990 being the latest). I assume there have been many substantial advancements since then. What ... |
I am looking for an efficient algorithm that lets me process the minimax search tree for chess with alpha-beta pruning on a distributed architecture. The algorithms I have found (PVS, YBWC, DTS see below) are all quite old (1990 being the latest). I assume there have been many substantial advancements since then. What ... |
Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?
From what I can tell from [wikipedia][1], the language needs to support recursion, or, seemingly, must be able to run without halting. Is this all there is to it?
[1]: http://e... |
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