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I'm very new to neural networks, and have been trying to figure some things out. So, let's say you come across a neural network which has 100 inputs, a hidden layer with 200 nodes, and 32 outputs. Let's also say that you, the "discoverer" of this particular instance of a neural network, are able to read the weights of... |
I think half the battle in answering this question lies in formulating it precisely! A search engine doesn't turn up much, so I was wondering if this is a well-known or well-studied question.
My thoughts: I think the most straightforward way to formulate this question is as in my title: Given constants $t,s,k \in \math... |
I am currently confused by the following situation:
1) The metric $k$-center problem is inapproximable in polynomial time within $2-\epsilon$ unless $P=NP$.
2) The metric $k$-center problem can approximated within $1+\epsilon$ in time $O(k^{O(k/ \epsilon)})$
Did I just win a million dollars or why isn't this a contra... |
I have two datasets that I am trying to match to one another. One dataset's contents is a subset of the other, but contains typographical errors of varying types and magnitude.
I am applying the following logic to the data linkage process:
Apply regular expressions in an iterative manner with increasing flexibility unt... |
I am learning the SVM classification and encounter a problem. I am not sure if this dilemma has a terminology for it.
Assume we would like to classify patient by SVM given the samples of healthy people ( of both gender) and people with liver cancer ( of both gender). If we label healthy people sample as class 1 and the... |
I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you think other tags would be more appropriate.
I am trying to solve this problem for which I need to compute the number of Hamiltonian cy... |
I'm trying to solve the following problem:
$$ 6AD3 - AF20 $$
Both of these are hex values in two's complement.
I keep getting one answer but it's turning out worng. What I tried to do, was take the complement of AF20, which I got as 50D1, and instead of subtracting, I added it to 6AD3, and I got BBA4, however, I am be... |
A homework assignment asks me to state the complexity in Big-O notation of the function
$$f(n) = 7n – 3n \log n + 100000 $$
I graphed this function and decreases all the way down to zero nearly its entire lifespan.
Therefore I concluded that the complexity is bounded by a constant and has the complexity $O(1)$.
Is th... |
Short version:
Is there an operator $\exists$ (on complexity classes) s.t. $\exists P = NP$ and $\exists REC=RE$, i.e. you can use the same operator on multiple interesting classes without explicitly stating a class of functions that limits the length of the witnesses?
The construction should not rely on the existence ... |
I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum.org but I'm still not sure if I have it right. I have the converting from a larger base to a smaller base down okay because it is simply t... |
I'm trying to understand the approach to constructing a PDA which accepts the language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ }
|
I have an algorithm which, basically given an array of $n$ numbers, checks if there is any repeated numbers in the array, and returns true if there is and false otherwise.
It uses a direct access table (hashing function $h(x)=x$), which makes the running time linear. So it creates a new array, initializes all values to... |
Here is the question:
Show that $L = \{0^m1^n : m > 1, n > 1, n < m \}$ is not regular.
I am not sure what superscripts mean in this situation? Does it mean something like this:
$0^5 = 00000$ or $1^7 = 1111111$.
|
If I had a Dijkstra graph with the number shortest paths from Node A to O being 1,
would it be correct to say: the equal number of shortest paths from A to O is 1 and not 0, because that node is included as an 'equal shortest path'? I am really confused.
Here is an image to illustrate my question:
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I don't know much about yacc, bison, flex or lex and please correct me if I'm wrong but a programming language is also a Turing machine and a Turing machine is defined as the tuple $(Q, \Gamma, b, \Sigma, \delta, q_0, F)$ where $Q$, $\Gamma$, $b \in \Gamma$, $\Sigma \subseteq \Gamma \smallsetminus \{ b \}$ as input, $\... |
Given an undirected unweighted multigraph $G=(V,E)$ and $s,t \in V$ find a simple $st$-path $P$ s.t. the number of edges leaving $P$ (i.e. the edges with exaclty one endpoint in $P$ ) is minimized.
Does anybody have any idea how to solve this?
I first thought about replacing edges by two arcs and weight them according... |
I don't know much when it comes to computers,
But If I wanted to learn how to programm algorithms that perform symbolic calculations and other techniques used to solve or aid mathematical problems, and to be able to classify the efficiency of different types of algorithms in terms
of different factors, what sub field ... |
Let $\Theta$ and $o$ be defined as usual (Landau-notation).
For two equivalence classes defined by $\Theta$ we define
$$\Theta(f) <_o \Theta(g) :\Leftrightarrow f \in o(g)\qquad.$$
Let $$\mathbb{F}:= \{\Theta(f)\mid f:\mathbb{N}\rightarrow\mathbb{N}\}$$
My question:
Is $\langle \mathbb{F},<_o\rangle$ Dedekind-complete,... |
I have a recurrence relation which is like the following:
$T(n) = 2T(\frac{n}{2}) + \log_{2}n$
I am using recursion tree method to solve this. And at the end, i came up with the following equation:
$T(n)=(2\log_{2}n)(n-1)-(1\times 2 + 2\times 2^{2} + \ldots + k\times2^{k})$ where $k=\log_{2}n$
I am trying to find a the... |
This question arises from my reading of "Types and Programming Languages" (WoldCat) by Benjamin C. Pierce.
For the small step operational semantic evaluation rules for the arithmetic expressions (NB) in Figure 3-2 on page 41, there is the rule
$pred\;(succ\;nv_1)\rightarrow\;nv_1$
My understanding is that it is to k... |
One of my lectures makes the following statement:
$$( f(n)=O(n) \land f(n)\neq o(n) )\implies f(n)=\Theta(n)$$
Maybe I'm missing something in the definitions, but for example bubble sort is $O(n^2)$ and not $o(n^2)$ but it's also not $\theta(n^2)$ since it's best case run time $\Omega(n)$.
What am I missing here?
|
I can think of functions such as $n^2 \sin^2 n$ that don't have asymptotically tight bounds, but are there actually common algorithms in computer science that don't have asymptotically tight bounds on their worst case running times?
|
I have a recurrence relation and trying to use master theorem to solve it. The recurrence relation is:
$T(n) = 3T(n/5) + n^{0.5}$
Can I use the master theorem in that relation? If so, can I say that $T(n)$ is $Θ(n^{0.5})$?
|
I have used FSM in Digital sequential Circuit designs. But I am unfamiliar with Finite Automata. Can somebody help me in understanding 'basic' difference between the two ?
|
I have a recurrence relation, it is like the following:
$T(e^n) = 2(T(e^{n-1})) + e^n$, where $e$ is the base of the natural logarithm.
To solve this and find a $\Theta$ bound, I tried the following: I put $k=e^n$, and the equation transforms into:
$$T(k)=2T(k/e)+k$$
Then, I try to use the Master Theorem. According to ... |
I am seeking help understanding Floyd's cycle detection algorithm. I have gone through the explanation on wikipedia (http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare)
I can see how the algorithm detects cycle in O(n) time. However, I am unable to visualise the fact that once the tortoise and hare pointers... |
I find it fairly easy to generate an upper bound for nearly any iterative solution (e.g. look at the limits on each loop, etc.), and can oftentimes create an upper bound for normal recursive functions.
However, I am now trying to determine a "Big-O" for a DP problem I've memoized. I don't really care about the answer ... |
This question arises from my reading of "Types and Programming Languages" (WorldCat) by Benjamin C. Pierce.
On page 36 is the definition for satisfied
A rule is satisfied by a relation if, for each instance of the rule,
either the conclusion is in the relation or one of the premises is
not.
On page 36 is the defi... |
I need to find a context-free grammar for the above expression, $a^{m}b^{n}$ for the set $L = \left\{{a, b}\right\}$, but I am having difficulty accounting for the condition $m \neq n$.
This is what I have so far, but it clearly doesn't satisfy the above condition:
$\begin{align}
&S \rightarrow aAb &\\
&S \righta... |
I've learned that a while loop such as
int i = 100;
while (i >= 1){
...
///Stuff
i = i/2
}
will run in logarithmic time, specifically, O(logn), since it keeps dividing in half each time (like a binary search).
However, what if my while loop looks like this
int i = 100;
while (i >= 1){
...... |
I'm trying to determine the complexity of this for loop:
for (int j =3; j <= n-2; j+=2) {
....
}
By trying out lots of examples, I came up with $\frac{n-4}{2} + 1$. This seems to work with every number now.
However, I am looking for a systematic and quick way to find these sorts of complexities. For example, can yo... |
I am not sure if this is the right forum to ask this.
I have some data of the houses, like their size(in square meters), if they use aircondition, how many residents live in, I have their electricity consumption as well.
I want to train any Machine Learning Algorithm to the dataset above, in order to create a model tha... |
I am studying computational theory with Sipser's textbook. I can't quite understand the definition of "reduction". For example, "this problem can be reduced to ATM ..."
What exactly does "to reduce" mean? I can't draw the picture in my head. Can anyone can help me understand this definition?
|
I am learning about information theory and mutual information. However, I am quite confused with MI(Mutual information) vs. PMI(Pointwise mutual information) especially signs of MI and PMI values. Here are my questions.
Is MI values a non-negative value or it can be either positive or negative? If it is always a n... |
CSP is used for the description and representation of concurrent systems, how it is used in practice (theoretically and programmatically)?
What are the application areas (other than concurrent and parallel systems) where it is used?
|
I am trying to understand how to do the amortized cost for a dynamic table. Suppose we are using the accounting method.
Let A of size m be an array of n elements. When $n = m$, then we create a new array of size $4m$, and then copy the elements of A to the new array. When $n = \frac{m}{4}$, then you create a new array ... |
I am studying MIT OCW lecture notes but they do not have solutions for the following problem.
Directed Acyclic Tournaments
In a round-robin tournament, every two distinct players play against each other
just once. For a round-robin tournament with no tied games, a record of who beat
whom can be described with a tourna... |
So I've been doing some reading on community detection in graphs as I'm planning on working on my thesis for it. I've been reviewing papers regarding the same and came across the Girvan-Newman algorithm. I've read the paper and have a doubt which I couldn't really figure out.
The algorithm works by removing the edge wh... |
Suppose $f(x)$ is a one way function. What about $h(x)=f(x_1) \, \oplus \,f(x_2)$, where $x=x_1 || x_2$ and $\lvert x_1 \rvert = \lvert x_2\rvert$?
$\oplus$ is exclusive disjunction (xor)
$||$ is concatenation
$|u|$ is the length of $u$
|
So I have been given the task of creating an PDA that recognises the language
$\{a^{2n} b^{3n} \mid n = 0,1,2,\dots\}$.
Am I right in thinking that it needs to have at least 3 times number of $b$'s than $a$'s?
So for example:
$aabbb$ would be accepted
$aaabb$ would NOT be accepted
However, how do I show that using JF... |
I have an input array and I have to select an indefinite number of intervals from it so that the "profit" is maximal and I have exactly T elements selected in total, where T is given. Profit means the sum of all the elements of an interval, except for the first element. An interval can consist of a single element, mean... |
Can the number of cycles in a graph (undirected/directed) be exponential in the number of edges/vertices?
I'm looking for a polynomial algorithm for finding all cycles in a graph and was wondering if it's even possible.
|
In my textbook, Data Structures and Algorithms in Java, the author says when implementing a queue using a linked list you choose the front of the queue to be at the head of the list, and the rear of the queue to be at the tail of the list. In this way, you remove from the head and insert at the tail.
The author then as... |
I have two languages $C_1$ and $C_2. \left(\Sigma=\{0,1\}\right)$:
$C_1=\left\{xyz\mid x,z \in \Sigma^*, y \in \Sigma^*1\Sigma^*, \text{ where } |x|=|z| \geq |y|\right\}$, and $C_2=\left\{xyz\mid x,z \in \Sigma^*, y \in \Sigma^*1\Sigma^*1\Sigma^*, \text{ where } |x|=|z| \geq |y|\right\}$
I want to show that $C_1$ is a ... |
A graph $G$ is chordal if it doesn't have induced cycles of length 4 or more. Chordal graphs are precisely the class of graphs that admit a clique tree representation. A clique tree $T$ of $G$ is a tree in which the vertices of the tree are the maximal cliques of $G$. An edge in $T$ corresponds to a minimal separator. ... |
Consider the following variant of the FACTORING problem (given N,M decide whether N has a prime factor less than M):
MULTIPLE-FACTORING: Given three integers $1 \leq K \leq M \leq N$ decide if there are at least $K$ prime factors of $N$ less than $M$
FACTORING $\leq_m$ MULTIPLE-FACTORING (just pick $K=1$) and
MULTIPL... |
I have to reduce $L_\text{empty}$ to $L_\text{inf}$
where
$\qquad L_\text{empty} = \{e \mid |L(P_e)| = 0 \}$ and
$\qquad L_\text{inf}= \{e \mid |L(P_e)| = \infty \}$.
where $P_e$ is the program with Gödel number $e$, and $L(P_e)$ the language it accepts.
So can I define a program $P$ like this
input n
Run Pe on 1...n ... |
If you have a dynamic array where the size $s$ becomes $4s$ when you fill the array and there are no delete operations. How much do you spend per insert?
I am asking because when the size doubles, you only spend 3 dollars per insert (based on this analysis). But when you make the size 4 times bigger, then for some of t... |
If you have an array that expands when it is completely filled and the new size is
N = N + 1 + ceiling(log2(N)) (N is the current size, and then N becomes the new size)
(log2 is log base 2).
How can you do an amortized analysis for this? It is confusing because the size of the expansion of the array increases as N inc... |
I am currently learning how randomised Hashing works.
So, you have a class (aka family) $H$ of hash functions, each of which maps the universe $U$ to the hash table $N$.
That class is called "strongly universal" or "pairwise independent" if $\forall x,y \in U, x \neq y: \forall z_1,z_2 \in N: \Pr\limits_{h \in H}[h(x)... |
I've read this part like 3-4 times and I'm not understanding what is going on.
Let G6 be the following CFG and convert it to Chomsky normal form by using the conversion procedure just given. The series of grammars presented illustrates the steps in the conversion. Rules show in bold have just been added. Rules shown i... |
I am looking for good resources which have classified and solved typical large scale data processing in MapReduce framework (like graph algorithms, statistics, numerical algorithms ...). Any help is appreciated!
|
Given a regular language $L$, can we say anything about its complement $\overline L$? One thing that is trivial to say is that the DFA's for both languages are equal in size as complementing the language is simply a matter of changing all accepting states into rejecting states and vice-versa. Are there any other things... |
Consider the interval scheduling problem, see also here.
In order to schedule the $n$ job requests over one resource, you sort the requests in order of finish time, choose the request with earliest finish time, choose the next compatible one, and so on.
Now, let us say we have two resources instead of one. How do I sch... |
I'm having a little bit of an issue with a pumping lemma problem. I've successfully completely all my other problems but this is the last one and I'm a little confused I must say. If anyone can help me out, it'd be much appreciated.
\begin{equation}
A = \{a^n b^m c^l \mid n\leq m \vee m\leq l\}
\end{equation... |
I am trying to calculate the amortized cost of a dynamic array, that's size becomes 4 times the size when the array is filled. (when you re-size, you create a new one and copy the elements there).
Here is what I am reading from. (starts at pg. 30)
This example has the array doubling when it is filled.
This is my potent... |
Is $L = \{ a^nb^nc^j \mid n \le j\}$ a context-free language? I'm getting really stuck generating a grammar for it. Any help would be appreciated.
|
I understand that context-free grammars can be used to represent context-free languages.It might have ambiguities. We also have normal forms like Chomsky and Greibach normal form. I couldn't understand the need of that.
Why they are important in the theory of languages? All the textbooks I referred to tell about these... |
Would it be correct to characterize loop invariants as a type of tautology? I ask since the invariant must basically always be true, before the loop starts, before each iteration and after the loop terminates. I realize that there is the possibility that the invariant could become false during the body of the loop. ... |
How do those matrices work? Do I need to multiple every single pixel? How about the upperleft, upperright, bottomleft and bottomleft pixels where there's no surrounding pixel? And does the matrix work from left to right and from up to bottom or from up to bottom first and then left to right?
Why does this kernel (Edge ... |
From the point of view of asymptotic behavior, what is considered an "efficient" algorithm? What is the standard / reason for drawing the line at that point? Personally, I would think that anything which is what I might naively call "sub-polynomial", such that $f(n) = o(n^2)$ such as $n^{1+\epsilon}$ would be efficie... |
Suppose that there is some graph, with $n$ vertexes. We wish to find the hamiltonian path, but we make the graph being searched a little different. There is a person A that travels each (undirected) edge that connects one vertex to the other vertex. But after the person crosses the edge, how edges connect pairs of vert... |
I have this very simple "proof" for NP = CoNP and I think I did something wrongly somewhere, but I cannot find what is wrong. Can someone help me out?
Let A be some problem in NP, and let M be the decider for A. Let B be the complement, i.e. B is in CoNP. Since M is a decider, you can use it to decide B as well (just f... |
A decision problem is NP-complete if it is in NP and all other problems in NP can be reduced to it by a reduction that runs in polynomial time. Why it is important to require that the reduction runs in polynomial time, as opposed to accepting any computable reduction.
|
I have some questions regarding local search / optimization as explained in chapter 4 of the book : http://aima.cs.berkeley.edu/
In classical search (Chap 3), the search starts from an initial node, then the search continues based on strategies of BFS, DFS, etc. What I am unsure of is the process of local search (Chap ... |
Given any graph $G$ on $V(G)=\{1,\dots,n\}$ and its adjacency matrix
$$A(G)=\left(\matrix{
A_{1,1} & A_{1,2} & \dots & A_{1,n}\\
A_{2,1} & A_{2,2} & \dots & A_{2,n}\\
&&\dots&\\
A_{n,1} & A_{n,2} & \dots & A_{n,n}
}\right)$$ any permutation on $\{1,\dots,n\}$ defines a new isomorphic graph $G'$. A common approach to ... |
I have a set of observations of real data, and a set of Random Variables I produce my self. The goal is to generated Random Variables with the same Distribution as the real data. To investigate the simliarity the two distributions, I use the Kullback-Leibler Divergence. Now with the genetic algorithm of Matlab, I try t... |
If I have a hash table of 1000 slots, and I have an array of n numbers. I want to check if there are any repeats in the array of n numbers. The best way to do this that I can think of is storing it in the hash table and use a hash function which assumes simple uniform hashing assumption. Then before every insert you ju... |
If I have a hash table of 1000 slots, and I have an array of n numbers. I want to check if there are any repeats in the array of n numbers. The best way to do this that I can think of is storing it in the hash table and use a hash function which assumes simple uniform hashing assumption. Then before every insert you ju... |
I am looking for an example of the "iterative lengthening search". I have searched and I was only able to find definitions like
iterative lengthening search an iterative analog to uniform cost
search. The idea is to use increasing limits on path cost. If a node
is generated whose path cost exceeds the current limi... |
A full binary tree seems to be a binary tree in which every node is either a leaf or has 2 children.
I have been trying to prove that its height is O(logn) unsuccessfully.
Here is my work so far:
I am considering the worst case of a full binary tree in which each right node has a subtree, and each left node is a leaf.
... |
Suppose $\sigma$ is a vocabulary of First Order logic consisting of one binary relation $E$ and let $\phi$ be a $\sigma$ sentence (FO formula with no free variables). Is it decidable whether there is a finite directed graph $G$, with all in- and out-degrees $0$ or $1$, such that $G\models \phi$ ?
|
I've found in many exercises where I'm asked to show that $f(n)=\Theta(g(n))$ where the two functions are of the same order of magnitude I have difficulty finding a constant $c$ and a value $n_0$ for the lower bound. I'm using Corman's definition of $\Theta$:
$$\exists c_1,c_2>0\in\mathbb{R}:\forall n\geq n_0: 0 \leq... |
I went to listen to a workshop and someone from the audience asked the presenter how the moments can improve the mutual information. I am learning about MI (Mutual Information) so didn't have enough knowledge to understand what it means. Then, I did some research but I still have some confusion. I am wondering if someo... |
I am wondering in general if it is correct to claim that if a special case of a problem is NP-Hard, the general case of that problem is NP-
Hard too?
For example: Min Set-Cover is NP-Hard does it imply without having to prove that Min Set-k-Cover where each element needs to be covered k times is NP-Hard too?
|
I'd like to start by stating this isn't homework! I'm studying for a job interview and would appreciate a second opinion. (Well, I guess it is homework, but not for school!).
I've written an algorithm (see pseudocode below) to merge two sorted lists into one sorted list. The problem requires that I implement it as a re... |
I have a kind of cutting problem. There is an irregular polygon that doesn't have any holes and a list of standard sized of rectangular tiles and their values.
I want an efficient algorithm to find the single best valued tile that fit in this polygon; or an algorithm that just says if a single tile can fit inside the p... |
It seems that (in a broad sense) two approaches can be utilized to produce an algorithm for solving various optimization problems:
Start with a feasible solution and expand search until constraints are tight and solution is maximal (or minimal).
Begin with violated constraints and search for maximal (or minimal) fe... |
When dealing with Landau notation, $\Theta, O,\Omega,o,\omega$, why do some texts choose the Corman style definitions, i.e.:
$$o(g(n))=\{ f(n): \forall c>0:\exists n_0>0:\; 0\leq f(n) < cg(n): \; \forall n\geq n_0 \}$$
and some texts use limit based definitions such as:
$$\lim_{n\to\infty}\frac{f(n)}{g(n)}=0\Rightarrow... |
I don't understand how the star1 variation mentioned in the paper is Sparse Sampling for Adversarial different than the usual star1 algorithm?
(Taken from the bottom of page 7). This variant can be easily
described in terms of the descriptions of Star1. To enable sampling,
one need only change the implementation o... |
A binary indexed tree has very less or relatively no literature as compared to other data structures. The only place where it is taught is the topcoder tutorial. Although the tutorial is complete in all the explanations, I cannot understand the intuition behind such a tree? How was it invented? What is the actual proof... |
Are there any "natural" examples of decidable problems that are definitively known not to be in NP? The decidable languages I know of that are not contained in NP are usually derived from the time hierarchy theorem, which produces "artificial" languages based on diagonalization.
|
Given two vectors of integers of possibly unequal lengths, how can I determine the maximum result possible from accumulating choosing the maximum between corresponding pairs of numbers between the two vectors with extra zeros inserted into the shorter vector to make up for the size difference?
For example, consider the... |
The problem: Only pattern-like images are supposed to be uploaded and be used as backgrounds to a site, photos should not. How would you detect if an image looks enough like itself to be regarded as a pattern?
|
Construct two functions $ f,g: R^+ → R^+ $ satisfying:
$f, g$ are continuous;
$f, g$ are monotonically increasing;
$f \ne O(g)$ and $g \ne O(f)$.
|
Is there any kind of CPU which doesn't contain an ALU ?
|
I want to prove that $E \subsetneq EXP$ and i would like to do so using the Time Hierarchy Theorem
I need to choose $f(n)$, i think $2^{cn}$ is a good choice, so here is my Proof:
$E\subseteq TIME(2^{cn})$
$TIME(2^{cn}) \subsetneq TIME(n^2 \cdot (2^{cn})^2)$ Time Hierarchy Theorem
$E \subsetneq EXP$
Is this correct ... |
I am looking for a way to implement division in modular arithmetic using modulo prime.
The method I found in math books is to try $u$ such that
$au \equiv 1 \pmod{p}$
$b/a \equiv bu \pmod{p}$
where $a, b, u \in Z_p$ (remainder class modulo a prime $p$). But trying things is probably not a good and fast approach (as it ... |
The goal is to distribute approximately 100 million variable length strings, average length 100 characters, uniformly among 100 million buckets. Perfection not required, just no egregious clumping. The strings are URLs. They tend to begin much the same way and end much the same way (e.g. h t t p:// or w w w. and ".c o... |
An exercise asks me to show that the Kleene star of any unary language $L$ is regular. $E$ is the alphabet, $E = \{ 1 \}$
Here's my reasoning :
$L$ is regular $\implies$ $L^*$ is regular (closure property)
$L$ is not regular
$L$ contains the word of length 1 $\implies$ $L^* = E^* \cup \{\epsilon\}$ $\implies$ $L^*$ i... |
I am struggling with a homework assignment. This next question seems to be pretty easy, once I get what I feel like I'm missing now. Anyway, here goes:
Decide if the following language is regular or not and prove your
claim.
$$L=\{a^{i_{1}}ba^{i_{2}}ba^{i_{3}}ba^{i_{4}}ba^{i_{5}}ba^{i_{6}}ba^{i_{7}}b|i_{1}>i_{2}>i_{... |
I wrote the following LL(1) grammar to describe the set of boolean expressions involving AND ,OR an NOT only. This, as can be seen, also reflects the precedence of the operators (ie., 'AND' is done before 'OR', etc).
Is it correct?
1. E ::= T E’
2. E’ ::= OR T E’
3. E’ ::= ε
4. T ::= F T’... |
How would I solve the following can anyone help me.I know MIPS is basically how many instruction the processor can do per second but what should I do?
Assume that we are receiving a message across a network using a modem with a rate of 56,000 bits/second. Furthermore assume that we are working on a workstation with an ... |
Does the difficulty of a strongly NP-hard or NP-complete problem (as e.g. defined here) change when its input is unary instead of binary encoded?
What difference does it make if the input of a strongly NP-hard problem is unary encoded? I mean, if I take for instance the weakly NP-complete Knapsack problem, it is NP-com... |
I have implemented Gaussian elimination for solving system of linear equations in the field of modulo prime remainders. If there is a pivot equal to zero I assume the system has no solution but how to calculate number of solutions of such systems when all pivots are non-zero? (i.e. one and more solutions)
|
How is Perfect shuffle a better interconnect scheme for parallel processing? For example if we consider a problem of sum reduction, I want to understand how this scheme is useful when implementing sum reduction in parallel , for example on a GPU?
|
An undirected graph is a near clique if adding an additional edge would make it a clique. Formally, a graph $G = (V,E)$ contains a near clique of size $k$ where $k$ is a positive integer in $G$ if there exists $S \subseteq V$ where $|S| = k$ and $u,v \in S$ where $(u,v) \not\in E$, and $S$ forms a clique in $(V,E \cup ... |
Is there a sequence of undirected graphs $\{C_n\}_{n\in \mathbb N}$, where each $C_n$ has exactly $n$ vertices and the problem
Given $n$ and a graph $G$, is $C_n$ an induced subgraph of $G$?
is known to be in class $\mathsf{P}$?
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I was reading the proof of pumping lemma from Sipser's book. I couldn't understand certain things mentioned there.
In the second paragraph he has written, "because $r_l$ occurs among first $p+1$ places, we have $l \le p+1$". Here, does $l$ denotes the number of states visited?
Also he wrote "We know that $j \neq l$, ... |
I'm trying to figure out what are currently the two most efficent algorithms that permit, starting from a Left/Right pair of stereo images created using a traditional camera (so affected by some epipolar lines misalignment), to produce a pair of adjusted images plus their depth information by looking at their disparity... |
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