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The recursion that I used in [my paper](http://www.springerlink.com/content/7722150064q64865/) "A linear-time algorithm for computing the Voronoi diagram of a convex polygon" by Aggarwal *et al* is also quite complicated.
Here is a description of the algorithm from our paper. In case it's not clear from the descrip... |
there is this question I read somewhere but couldn't answer it myself.
I have an LR(1) Parsing table. Is there anyway that just by looking at it and the items, can we deduce that it is also a table for LALR and SLR?? |
From the LR(1) parsing table, can we deduce that it is also an LALR and SLR table? |
|grammars| |
It is known that each optimization/search problem has an equivalent decision problem. For example,
> The Shortest Path Problem:
>- **optimization/search version:**
> Given an undirected unweighted graph $G = (V, E)$, and two vertices $v,u\in V(G)$;
> Find a shortest path between $v$ and $u$.
>- **decision vers... |
Optimization version of decision problems |
|optimization| |
|complexity-theory|optimization|search-problem|decision-problem| |
An algorithm is a finite description of a computational process that transforms input data into output data.
Questions tagged with [tag:algorithms] typically ask for an [algorithm](http://en.wikipedia.org/wiki/Algorithm) to solve a specific task, or ask for an analysis of a given algorithm (note also [tag:algorithm-... |
null |
Use this tag if you want to be given hints, not full answers. |
null |
Trivially, yes: the grammar is extractible from the items.
Probably more in the spirit of the question. LALR(1) is easily extractible from LR(1): merge LR(1) items which correspond to the same LR(0) one and the grammar isn't LALR(1) if that process results in conflicts. (BTW this can be considered as a definition of... |
Let $\mathrm{SDL}_k$ the *shuffled Dyck language with $k$ types of parentheses*, i.e.
$\qquad \displaystyle \mathrm{SDL}_k = \mathrm{DL}([_1,]_1) \, ш\, \dots \, ш\, \mathrm{DL}([_k,]_k)$
with $ш$ the [shuffle](https://en.wikipedia.org/wiki/Shuffle_product) of languages and $\mathrm{DL}(\_,\_)$ the [Dyck language... |
It is known that each optimization/search problem has an equivalent decision problem. For example the shortest path problem
>- **optimization/search version:**
> Given an undirected unweighted graph $G = (V, E)$ and two vertices $v,u\in V(G)$, find a shortest path between $v$ and $u$.
>- **decision version:**
> ... |
There is this question I read somewhere but could not answer myself.
Assume I have an LR(1) Parsing table. Is there any way that just by looking at it and its items, can I deduce that it is also a table for LALR and SLR? |
|parsers| |
Trivially, yes: the grammar is extractible from the items.
Probably more in the spirit of the question. LALR(1) is easily extracted from LR(1): merge LR(1) items which correspond to the same LR(0) one and the grammar isn't LALR(1) if that process results in conflicts. (BTW this can be considered as a definition of L... |
My favorite recurrence shows up in output-sensitive algorithms for computing convex hulls, first by [Kirkpatrick and Seidel](http://en.wikipedia.org/wiki/Kirkpatrick%E2%80%93Seidel_algorithm), but later repeated by others. Let $T(n,h)$ denote the time to compute the convex hull of $n$ points in the plane, when the con... |
null |
Let $\mathrm{SDL}_k$ the *shuffled Dyck language with $k$ types of parentheses*, i.e.
$\qquad \displaystyle \mathrm{SDL}_k = \mathrm{DL}([_1,]_1) \, ш\, \dots \, ш\, \mathrm{DL}([_k,]_k)$
with $ш$ the [shuffle](https://en.wikipedia.org/wiki/Shuffle_product) of languages and $\mathrm{DL}(\_,\_)$ the [Dyck language... |
Let $\mathrm{SDL}_k$ the *shuffled Dyck language with $k$ types of parentheses*, i.e.
$\qquad \displaystyle \mathrm{SDL}_k = \mathrm{DL}([_1,]_1) \, ш\, \dots \, ш\, \mathrm{DL}([_k,]_k)$
with $ш$ the [shuffle](https://en.wikipedia.org/wiki/Shuffle_product) of languages and $\mathrm{DL}(\_,\_)$ the [Dyck language... |
As already stated in the comments, it depends on the definitions, as usual. My attempt to answer this needs quite a few definitions, so this will be another example of my inability to give concise answers.
Def: An *optimization problem* is a tuple $(X,F,Z,\odot)$ with
- $X$ the set of suitably encoded (strings) ... |
null |
{"Voters":[{"Id":69,"DisplayName":"Patrick87"}]} |
{"Voters":[{"Id":69,"DisplayName":"Patrick87"}]} |
I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called *min-heap automata*; the original question, and links to others, can be found [here][1].
This question concerns the computational power of type-2 min-heap automata, which were suggested by Raphael as ... |
I have asked a series of questions concerning capabilities of a certain class of exotic automata which I have called min-heap automata; the original question, and links to others, can be found [here][1].
Two of my last questions seem to have been quickly dispatched; one completely, and the other mostly (I have edite... |
Power of nondeterministic type-1 min-heap automaton with both a heap and a stack |
|formal-languages|automata| |
*See the end of this post for some clarification on the definition(s) of min-heap automata.*
One can imagine using a variety of data structures for storing information for use by state machines. For instance, push-down automata store information in a stack, and Turing machines use a tape. State machines using queues... |
According to wikipedia:
>Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained representation of that string.
What is the analogous informal rigorous definition of "useful information"? Why is "us... |
Difference between "information" and "useful information" in algorithmic information theory |
|information-theory| |
The central concept here is [Kolmogorov complexity](http://en.wikipedia.org/wiki/Kolmogorov_complexity), and more specifically [compressibility](http://en.wikipedia.org/wiki/Incompressible_string). To get a intuitive feeling of compressibility, consider two strings $A \in \mathbb{B}^*$ and $B \in \mathbb{B}^*$, where $... |
According to [Wikipedia](http://en.wikipedia.org/wiki/Algorithmic_information_theory#Overview):
>Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained representation of that string.
What is the an... |
|information-theory|kolmogorov-complexity| |
null |
It could be because "useful" is hard to define. Say we have a highly-structured, information-rich message $x$ which can be compressed at most by a factor of $\alpha$ to the message $y$. Intuitively, $x$ and $y$ contain the same amount of useful information; indeed, they contain the same amount of information according ... |
The central concept here is [Kolmogorov complexity](http://en.wikipedia.org/wiki/Kolmogorov_complexity), and more specifically [compressibility](http://en.wikipedia.org/wiki/Incompressible_string). To get a intuitive feeling of compressibility, consider two strings $A \in \mathbb{B}^*$ and $B \in \mathbb{B}^*$, where $... |
null |
The central concept here is [Kolmogorov complexity](http://en.wikipedia.org/wiki/Kolmogorov_complexity), and more specifically [compressibility](http://en.wikipedia.org/wiki/Incompressible_string). To get a intuitive feeling of compressibility, consider two strings $A \in \mathbb{B}^*$ and $B \in \mathbb{B}^*$, where $... |
My favorite recurrence shows up in output-sensitive algorithms for computing convex hulls, first by [Kirkpatrick and Seidel](http://en.wikipedia.org/wiki/Kirkpatrick%E2%80%93Seidel_algorithm), but later repeated by others. Let $T(n,h)$ denote the time to compute the convex hull of $n$ points in the plane, when the con... |
I still don't really understand what you mean by "sophisticated recursion". For example, the recursion step in the FFT algorithm is sophisticated!
But if you want to look for more *complicated* recursion, then [mutual recursion][1] might be one possible answer. Mutual recursion is useful when working with [fuctiona... |
The recursion that I used in [my paper](http://www.springerlink.com/content/7722150064q64865/) "A linear-time algorithm for computing the Voronoi diagram of a convex polygon" by Aggarwal *et al* is also quite complicated.
Here is a description of the algorithm from our paper. In case it's not clear from the descrip... |
null |
As already stated in the comments, it depends on the definitions, as usual. My attempt to answer this needs quite a few definitions, so this will be another example of my inability to give concise answers.
---
**Definition:** An *optimization problem* is a tuple $(X,F,Z,\odot)$ with
- $X$ the set of suitably en... |
As the comments say, the answer depends on the exact definitions.
Let me interpret the question in a very basic (even naïve) way.
Let $S$ be some relation, that is $S \subseteq \{ (a,b) \mid a,b \in \Sigma^*\}$.
Now we define a **search problem** for $S$:
> Given $a$, find a $b$ such that $(a,b) \in S$.
and... |
The central concept here is [Kolmogorov complexity](http://en.wikipedia.org/wiki/Kolmogorov_complexity), and more specifically [compressibility](http://en.wikipedia.org/wiki/Incompressible_string). To get a intuitive feeling of compressibility, consider two strings $A \in \mathbb{B}^*$ and $B \in \mathbb{B}^*$, where $... |
Off the top of my head, the [McCarthy 91 function](https://en.wikipedia.org/wiki/McCarthy_91_function)
F(N) =
n - 100 if n > 100
F(F(n+11)) if n <= 100
and the [Ackermann function](https://en.wikipedia.org/wiki/Ackermann_function)
A(m, n) =
n + 1 if m = 0
... |
null |
Patrick87 explained this all very well. But one additional optimization you could make would be to use something like a circular buffer: you can move items right of the position of the inserted element to the right, as usual. But you can also move items to the left of the correct position to the left. To do this, you n... |
A question in some formal system with a yes-or-no answer. |
null |
An image generation method that works by tracing the path of light through the pixels in an image. |
null |
Methods of estimating the increase in the run-time of an algorithm as the input size increases. |
null |
Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to think about different types of problems, and different fields use different formulation for this reason.
When I work... |
Quantum lambda calculus |
|quantum-computing|functional-programming|reference-request| |
|quantum-computing|reference-request|model-of-computation| |
|complexity-theory|efficiency|model-of-computation| |
This a homework question from Udi Manber book. Any hint would be nice :)
I must show that:
**n*(log3(n))^5 = O(n^1.2)**
I tried using Theorem 3.1 of book:
f(n)^c = O(a^f(n)) (for c > 0, a > 1)
Substituing:
(log3(n))^5 = O(3^log3(n)) = O(n^log3(3)) = O(n)
but n*(log3(n))^5 = O(n*n) = O(n^2) != O(n^... |
Is n(log3(n))^5 = O(n^1.2)? |
|algorithms|complexity-theory|algorithm-analysis|runtime-analysis| |
|quantum-computing|turing-machines|model-of-computation| |
This a homework question from Udi Manber book. Any hint would be nice :)
I must show that:
>$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*n) = O(n^2) \ne ... |
|asymptotics| |
How to prove that $n(\log_3(n))^5 = O(n^{1.2})$? |
This a homework question from Udi Manber 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(n^2) \... |
Do what you did, but let $a = (3^{0.2})$... that should do it, right? |
Do what you did, but let $a = (3^{0.2})$... that should do it, right?
EDIT: The reason that what you did didn't work is as follows. The big-oh bound is not tight; while the logarithm to the fifth is indeed big-oh of linear functions, it is also big oh of the fifth root function. You need this stronger result (which ... |
|quantum-computing|model-of-computation|lambda-calculus|reference-request| |
|asymptotics|mathematical-analysis| |
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