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I see how objects in a category stand for types, but where do I find the terms and more specifically the rules which tell me which of them are allowed? When I e.g. consider a Cartesian closed category as model of a type theory, how are term constructors represented?
I guess this is the same as asking how do I know or ... |
Would I use the third case of the Master Theorem for the recurrence equation $T(n) = 2T(n/2) + n^{2}\log n$?
The condition given for the third case by Wikipedia is $f(n) = \Theta(n^c)$ when $c > \log_{b}a$.
|
Some researchers are trying to get a memory cell capable of having 3 states instead of 2.
1) How many memory cells, in principle and as a rough estimate, does a typical 1 megabyte memory chip has? is it 8*1024 cells?
2) If you have N memory cells, each has x logical levels, what is the number of possible representation... |
Neural networks can have multiple inputs.
But some times two or more of these inputs can often be related to a single entity.
E.g : Height and weight of a person to predict the probability of disease or price and Volume of a stock to predict it's value.
How can we make a neural network understand that two inputs are re... |
Background: The Exact-3D-Matching problem is defined as follows (The definition is from Jeff's lecture note: Lecture 29: NP-Hard Problems. You can also refer to 3-dimensional matching):
Exact-3D-Matching: Given a set $S$ and a collection of three-element subsets of $S$, called triples, is there a sub-collection of dis... |
I have a question regarding recursion in Viterbi algorithm.
Define $\pi(k; u; v)$ which is the maximum probability for any sequence of length $k$, ending in the tag bigram $(u; v)$.
The base case if obvious $\pi(0,*,*)=1$
The general case.
$\pi(k,u,v) = max_{w \in K_{k-2} } \pi(k-1,w,u) \cdot q(v|w,u) \cdot e(x_k|v)$
... |
I'm trying to understand why the sorting algorithm Selection Sort has asymptotic runtime in $O(n^2)$.
Looking at the math, the runtime is
$\qquad T(n) = (n-1) + (n-2) + \dots + 2 + 1$.
And this is stated to be equal to
$\qquad O(n^2)$.
However I just don't understand the intuition. I have tried several practical experi... |
I've created a data structure that is a hash of arrays with a special property: the hash keeps track of the combined order in which items are appended to its arrays.
For example (pseudocode):
h = HashOfArray()
h["a"].append(1) // accessing an unset key returns an empty array
h["b"].append(2)
h["a"].append(3)
h["b"].a... |
I want to use “Fingerprint matching using multi-dimensional ANN”
by Rajesh Kumar and B.R. Deva Vikram [content link] for fingerprint identification. But I have a serious problem understanding what is a Multidimensional Artificial Neural Network.
I searched for keywords MDANN and Multidimensional ANN but I can't find an... |
I have a question regarding optimal mistake bound for learning algorithm
There is a famous fact that $VC(C) \leq Opt(C)$,
where $C$ - set of learning concepts,
VC(C) - VC dimension of C,
$Opt(C)$ - the smallest mistake bound (of the best learning algorithm) on the hardest learning concept $c \in C$ .
I don't understan... |
Relevant Information:
Sieve of Eratosthenes
Sieve of Sundaram
Suppose I want to generate all primes in [2,n], and I have both of these algorithms at my disposal to get the job done. Which is preferable under what conditions?
I read that Sundaram runs in O(n log n) time, whereas Eratosthenes runs in O(n log log n) time,... |
I understand that MESI is a subset of the MOESI cache coherency protocol. But what does the Owned state in the MOESI protocol represent? What are the differences in state transition due to the extra Owned state in MOESI as compared to MESI?
For example consider same cache line in processor P1 is in OWNED state & proce... |
You probably know this one (or at least a version of it).
Let $P$ be a program code, and $w$ be an input string.
Define $A_{TM}=\left\{(P,w)| P(w)=1\right\}$.
Meaning: $A_{TM}$ is the set of all ordered pairs $(P,w)$ s.t. $P$ accepts $w$.
$A_{TM}$ is undecidable.
I just read the proof for it, that made me wonder about ... |
I tried, but I could not design a turing machine for the following problem:
Turing machine that takes as input a tape containing a series of n 1s,
where n >= 0, terminated by an = sign. The Turing machine head is initially positioned on
the leftmost 1. The end state should be a tape containing the input, followed by th... |
I need to show that the language Anfa = {(A,w)| A is an nondeterministic finite automata that accepts w} can be decided in polynomial time. My problem is every solution that I think of requires exponential time.
I would appreciate any help, Thanks in advance..
|
I'd like to have this feature in my application programming language (which these days, is Scala), but when I went to learn more about it on the internets, I realized I don't know the name of it. I'm talking about the ability to do this (in Scala-ish pseudocode):
// Define some types that correspond to table rows in r... |
Philip Wadler has written a brilliant paper called 'Theorems for Free'. The big idea is that you can use types to reason about your program, and even prove simple theorems about your program.
We see these ideas about types applied in the Haskell language.
At very roughly the same time period - we have an idea from Be... |
I am curious whether the following problems has been studied before, but wasn't able to find any papers about it:
Given a planar graph $G$, and two vertices $s$ and $t$, find an
$s$-$t$ path $P$ which minimizes the number of distinct faces of $G$
containing vertices of $P$ on their boundaries.
Does anybody know a... |
I am trying to describe a TM that decides the language $A=\{0^{5^n} \mid n\ge0\}$.
I know how to do this for $0^{2^n}$, marking off every other 0 in each pass. In my case would it work marking off every fifth 0 in each pass? It would reject if there are an even number of 0s. Every pass reduces the number of 0's by a fi... |
From what I have learned asymptotically tight bound means that it is bound from above and below as in theta notation.
But what does asymptotically tight upper bound mean for Big-O notation?
|
I'm using machine-learning algorithms to solve binary classification problem (i.e. classification can be 'good' or 'bad'). I'm using SVM based algorithms, LibLinear in particular. When I get a classification result, sometimes, the probability estimations over the result are pretty low. For example, I get a classificati... |
Define the language $L$ as $L = \{a, b\}^* - \{ww\mid w \in \{a, b\}^*\}$. In other words, $L$ contains the words that cannot be expressed as some word repeated twice. Is $L$ context-free or not?
I've tried to intersect $L$ with $a^*b^*a^*b^*$, but I still can't prove anything. I also looked at Parikh's theorem, but ... |
While reading an article on logic, there is a sentence "No number is equal to zero" and we have to assign truth values to this sentence. I hope this is true and the article says it as false.
Can someone explain me why it is false? Or the author of the article is wrong?
|
I found this problem in a book. It supposedly minimizes the number of Support vectors rather than maximizing the margin:
$min_{\alpha,b} \frac{1}{2}\sum_{i=1}^{m}\alpha_{i}^{2}$
$s.t.\quad y_{i}(\sum_{j=1}^m\alpha_{j}y_{j}(x_{i}\cdot x_{j})+b)\ge1 \quad \forall i\in \{1,...m\}$
(for simplicity, I've omitted the slack v... |
I want to use the pumping lemma to show that the following language is not context free:
$$
L = \{w \in \{a,b\}^* \mid \exists d \in \{a,b\}^*, w=ddd \}
$$
We suppose that $L$ is context-free. Then from the pumping lemma there is a pumping length $p$. Which word $s$ do I have to use, that belongs to $L$ and such that... |
there are many classes of graphs proved GI complete & many questions related to GI on tcs.se eg [1] & many others.
suppose a class both $X$ and not-$X$ of graphs are proven GI complete. what are the implications of that?
[1] open problems related to GI
|
Is there an efficient way to cluster nodes in a graph using Jaccard similarity such that each cluster has at least k nodes?
Jaccard similarity between nodes i and j: Let S be the set of neighbours of i and T be the set of neighbours of j. Then, the similarity between i and j is given by $\frac{|(S \cap T)|}{|(S \cup ... |
I recently had a lengthy exchange with someone about the most efficient way to remove duplicates from a collection. The debate was mostly centered around the specific behavior of C# collections, such as HashSet(T) and HashTable(T).
I think we agreed on the fundamentals, but where we couldn’t come to an agreement was w... |
I'm trying to understand decidable languages. In particular, I would like to show that
$$B = \lbrace \langle D \rangle \mid \exists k \geq 0 \,.\,\text{DFA $D$ accepts $a^k b^k$}\rangle.$$
I don't quite understand the process of proving these. I know that $a^kb^k$ is not regular, so then no DFA accepts it. I also know ... |
I have some difficulties in understanding the intuition behind Naive Bayes Classification.
In general, I do understand every argument of the definition, however I don't understand why it's correct and why any other argument is incorrect.
Start from the beginning:
Goal: $v_{MAP} = argmax_{v_i} p(v_i|a_1...a_n)$
the goal... |
I cannot conceive of any problem that can be solved in exponential time, but cannot be checked in polynomial time.
|
I have the following CFG which I suspect cannot be rewritten to one which is LL(1):
$S \rightarrow \epsilon\ |\ aSbS\ |\ bSaS\ |\ cSdS\ |\ dScS$
I've thought about it for a while, and can't seem to make any progress. I know that the simpler grammar here can be rewritten into LL(1), but it seems like there is something ... |
Not sure if I should ask it here but I'll just go ahead. I was reading SICP (Structure and Interpretation of Computer Programs). And there was one quote from Alan Perlis in the preface to the second edition.
Is it possible that software is not like anything else, that it is meant to be discarded: that the whole point ... |
Given array $A = \{ a_{1},a_{2}, ..., a_{n}\}$ and integer $k; 0 \lt k \le n$, partition array $A$ into $k$ subarrays, such that
$A'_{1} = \{a_{1}, ...,a_{x}\}$
$A'_{2} = \{a_{x+1},...,a_{y}\}$
$...$
$A'_{k} = \{a_{z+1},...,a_{n}\}$
where each subarray $A'_{1},A'_{2}, ...,A'_{k}$ has sum of its elements closest to $\si... |
Say I have Simply typed lambda calculus, and add an assignment rule:
<identifier> : <type> = <abstraction>
Where <identifier> is the name of the function, <type> is the function type and <abstraction> is the abstraction to be assigned to the identifier.
Then I add a typing rule that says that when you see an assignme... |
Let's assume that I've implemented a method for the extraction of the principal lines of the palmprint. For instance, let's say that I'm able to do a transformation like the following one (image from Patprapa Tunkpien, Sasipa Panduwadeethorn and Suphakant Phimoltares):
Now, I want to make an evaluation of the accuracy... |
The conclusion follows from all the premises. It seems to me that this means that conclusion from the conjuntion of the premises. Right? Why does logic uses comma instead?
|
This question was originally posted here: https://stackoverflow.com/q/20735339/2305618
I am surely not the first to have implemented code to perform the following graph transformation. But try as I might, I can't find a previous reference to it.
The transformation arises when creating a single graph that simultaneousl... |
Iam a beginner in Lambda Calculus, I have a expression
saying
(λx.xy)
Here y is a free variable and x is a bound variable. My question is what would be the value of the expression (which has free variables).
|
I got stuck in Ladner's Proof while reading "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak. Pardon me if I'm missing something really obvious here but the authors do the following:
For every function $H\colon\mathbb{N}\to\mathbb{N}$ define
$$SAT_H=\{\psi01^{n^{H(n)}}: \psi \in SAT \ and \... |
I am working on a special case of the longest path problem. For a cyclic directed graph $G=(V, E)$, where the edge-weights are probability values (i.e., $P(\_) = w(s, q)$ with $s,q \in V$), my aim is to find the least 'probable' path between two vertices.
My initial approach is to generate an graph $G'$ where the weig... |
Is the complexity class $P$ closed under rotation, where rotation is defined as $\text{rot}(L) = \{ wv \mid vw \in L \}$? How would we prove it?
|
Given an undirected weighted graph $G(V,E)$, where the number of edges is $|V|+10$, how can I find the minimum spanning tree of $G$ in $O(|V|)$?
Kruskal's algorithm is out of the question, since sorting alone is $O(|V|\log |V|)$, so I thought maybe using Prim's algorithm with minimum binary heap, but still - every iter... |
I am looking for an algorithm to solve the following problem:
INPUT: a set of $n$ points in the plane, $(x_1,y_1),...,(x_n,y_n)$.
OUTPUT: a set of $n-1$ axis-parallel interior-disjoint squares, such that the boundary of each square contains at least two points. (*)
Here is an example of input (left) and possible output... |
A link to the transcript of the manuscript: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/EWD1300.html
My questions:
What does Dijkstra mean by:
"Do not introduce priority [precedence] rules that destroy symmetry. I remember how
much more pleasant the predicate calculus became to work with after we
ha... |
As I understand, to show that a certain problem $P$ is NP-hard we can reduce a known NP-hard problem $Q$ to a problem in $P$. This reduction, say $f$, has to be polynomial time.
Could someone please explain is it necessary that $f$ maps each instance of $q\in Q$ to $P$ or can we map a selected subset of $\tilde Q \s... |
When we say a problem is NP-hard is that a property of a set of problems or is it a property of a instance of the set of problems?
|
Self-stabilizing algorithms are extremely useful in distributed systems,
but can the algorithm be applied concurrently to each computational node?
My instinct is to say yes, but I can't help but imagine a 'Game Of Life' scenario
where the state of the graph toggles between two states.
What keeps the question alive ... |
The proofs that the halting problem is undecidable seem to make very few assumptions about the kind of program/machine under consideration: just that the programs take one input and either loop or produce an output. Not just Turing machines have these characteristics: for example, a linear-bounded automaton can also lo... |
I have a image similar to below. In that I need to find all red circles and count them.
So, I am thinking to use MATLAB R2011a with Image Processing Toolkit for it. How could I possibly extract them?
|
Suppose a parameter $\hat{k}$ is larger than another parameter $k$, assume that $k$ is bounded
by a function $f$ of $\hat{k}$.
How can we prove that if a problem is FPT with respect to $k$ implies it is FPT w.r.to $\hat{k}$.
|
I came accross the question regarding program overlays,
Program1 is of 100kB and program2 is of 90kB and common code is 10kB and overlay driver is 20kB and error handling routine is 50kB, min memory required when there is no error?
according to me it should be 100 + 20 + 10 = 130; as there is no error..
but ans is 1... |
Given simple, udirected and connected graph with $n$ verticies. Every edge in this graph has some weight. I have to find (in polynomial time) a set of edges such that :
1.every simple cycle in graph contains at least one edge from this set
2.sum of weights of these edges is the least possible
I have derived the fol... |
Let G be a weighted undirected graph and e be an edge with maximum weight in G.Suppose there is a minimum weight spanning tree in G containing the edge e.Which of the following statements is always TRUE?
1.There exists a cut in g having all edges if maximum weight
2.There exists a cycle in G having all edges of maximum... |
I am trying to construct all inequivalent $8\times 8$ matrices (or $n\times n$ if you wish) with elements 0 or 1. The operation that gives equivalent matrices is the simultaneous exchange of the i and j row AND the i and j column. eg. for $1\leftrightarrow2$
\begin{equation}
\left( \begin{array}{ccc}
0 & 0 & 0 \\
0 & 1... |
Suppose I want to run Dijkstra's algorithm on a graph whose edge weights are integers in the
range 0, ..., W, where W is a relatively small number.
How can I modify that algorithm so that it takes time just O((|V| + |E|) logW) and relatively easy implement that in C/C++?
|
T (n) = T(√n) + 1
The easy way to do this is with a change of variables. Let m = lg n and
S(m) = T (2^m).
T(2^m) = T (2^(m/2)) + 1
S(m) = S(m/2) + 1
Can any one explain why 1 and 2 are same and this works ??
|
Algorithms for the finding of an MST in a graph can be applied for both maximum and minimum spanning trees.
It is well known, however, that the finding of a max-cut in a graph is an NP-hard problem while the min-cut problem can be easily solved in polynomial time.
Why aren't the two equivalent?
What is the restriction... |
Context-free languages are not closed under complementation. In the lectures we have been given the same argument as here on Wikipedia: For
$$A = \{\mathtt a^n \mathtt b^n \mathtt c^m;~m, n ∈ ℕ_0\}\quad\text{and}\quad B = \{\mathtt a^m \mathtt b^n \mathtt c^n;~m, n ∈ ℕ_0\},$$
both $A$ and $B$ are context-free, but thei... |
The PARTITION problem is NP-complete:
INSTANCE: finite set $A$ and a size $s(a) \in \mathbb{Z}^+$ for each $a \in A$
QUESTION: Is there a subset $A' \subseteq A$ such that $\sum_{a \in A'} s(a) = \sum_{a \in A \setminus A'} s(a)$
The problem remains NP-complete even if the elements are ordered as $a_1,a_2,...,a_{2n}$ ... |
Consider an instance of TCP’s Additive Increase Multiplicative Decrease(AIMD) algorithm where the window size at the start of the slow start phase is 2 MSS and the threshold at the start of the first transmission is 8 MSS. Assume that a time out occurs during the fifth transmission. Find the congestion window size at t... |
Given two sets A and B of sizes |A| = n and |B| = m, where m >= n.
There are edges from set A to set B.
I need to find the number of matchings where all of vertices in set A have been matched with one vertex in set B.
Is it possible to caclulate this quantity ?
(I have very little knowledge of Graph Thory and Bipartite... |
I have got some equipment of standard lengths, say:
equipment_lengths = {60, 48, 36, 29}
that I have to place on a given length of, say 100. I have to place this equipment so as to minimize material waste while covering the given length. I am allowed to exceed the given length of 100 but keep the excess minimized. ... |
Suppose we are given matrices $A_1, \ldots, A_k$ which are $n \times n$ matrices with rational entries and are asked to determine whether the polynomial ${\rm det}(\alpha_1 A_1 + \alpha_2 A_2 + \cdots + \alpha_k A_k)$ is identically zero. How can we do this deterministically in polynomial time in $n$ and $k$?
I'm aware... |
I am looking for a reference for the following theorem:
Let $G$ be a bipartite graph with partitions $X$ and $Y$, each with the same number of vertices ($n$).
There is a nonempty subset $Y_1 \subseteq Y$, and a partition of $X$ to disjoint subsets $X_1$ and $X_2$, such that:
There is a complete matching between $X_1$ ... |
As described in this paper, you can use an pre-computed automaton to speed up an Earley parse. I'm not interested in the rigorous proof of this, but just how the basic algorithm works so that I can implement it. Understanding this paper on my own would take a long long time, and I don't think it's justified for this ... |
This question was asked in the onsite regionals for ACM ICPC 2013 at Amritapuri.
In short, the question asked to find the number of ways to fill a $ 2\times N$ grid with $M$ colors such that no two cells with the same row or same column have the same color.
The limits given are $1 \leq N$, and $M \leq 1000$ with 1000 t... |
I know that standard Bloom Filters only have operations like inserting elements and checking if an element belongs to filter, but are also some modification of Bloom filters which enable a delete operation--for example: counting Bloom filters. I heard also about another method, which uses a second filter. If I want to ... |
In a database system, say there are $N$ transactions each having $m_1,m_2,\dots,m_N$ operations. How many concurrent schedules are possible?
$(m_1+m_2+....+m_n)!$ is the number of possible interleavings.
Is this number equal to number of concurrent schedules? Serial schedules have to be discarded from the total number... |
In various discussions of the merits of functional programming, the phrase referential transparency or equational reasoning is often listed.
My question is - are these roughly the same thing? (One being the concept, and the second being the process of applying the concept?
|
Given are a 2D plane and a array of points in this plane, with every point having an integer value assigned.
Is there an algorithm which, when given a ratio a/b, divides the plane with a straight line, so that the values of the points are distributed as close as possible to the given ratio?
Points may be on the dividi... |
Does anyone know a good algorithm for quickly finding an approximate solution to the following problem?
Given two square matrices $A$ and $B$, minimize $\| P A P^\top - B \|$ over all permutation matrices $P$.
I have heard that there are several types of algorithms for these kinds of problems, like iterative improvemen... |
Is there any example that anybody could come up with that shows Prim's algorithm does not always give the correct result when it comes knowing the minimal spanning tree.
|
I'm both asking for me & future readers as to how pictures, sounds, textures, assets, and such are compiled and linked in to one binary/program, and how that process works.
I have seen this in standalone programs I have downloaded on Windows, and I'm fairly certain any OS can implement this. It appears that, instead of... |
I am getting confused with the solution to this recurrence -
$T(n) = T(n/2) + n^2$
Recursion tree -
T(n) Height lg n + 1
|
T(n/2)
|
T(n/4)
So it turns out to be -
$T(n) = n^2(1 + 1/4 + (1/4)^2) + \ldots (1/4)^{\log_2 n - 1})$
$T(n) = 4*n^2(1- (1/4)^{\log_2 n})/3 + n^2 $
$T(n) = 4*n^2(1 - 1^{\l... |
Lets assume $P = NP$. Can we say if every language $L \in P$, then $L \in NPC$?
I read $P \subseteq NP$, which means that $L\in NP$. So I know for example, that a language can be $NP \text{ hard}$, but it doesn't have to be in $NP$, e.g. $HALT$.
But what about the case above. Is the language also $NPC$?
|
An exercise that was in a past session is the following:
Prove that there exists an undecidable subset of $\{1\}^*$
This exercise looks very strange to me, because I think that all subsets are decidable.
Is there a topic that I should read to find a possible answer?
|
Given integers $n,m$, I want to find a $m \times n$ binary matrix $X$ such that there does not exist any non-zero vector $y \in \{-1,0,1\}^n$ with $Xy=0$ (all operations performed over $\mathbb{Z}$). What algorithm could I use for this?
In more detail: We are given parameters $n$ and $m$. The problem is to determine... |
This is more of a conceptual question.
I have learned about Neural Nets, and I have some clue as to how Support Vector Machines work. I read somewhere however that given the appropriate kernel (is that right?), the SVM is identical to the Neural Net. Could someone who understands this please enlighten me as to how that... |
Background:
In the book of Principles of Model Checking (Christel Baier and Joost-Peter Katoen, MIT Press, 2007), Section 9.2, page 701, the semantics of the until modality is defined over some time-divergent path $\pi \in s_0 \Rightarrow^{d_0} s_1 \Rightarrow^{d_1} \cdots \Rightarrow^{d_{i-1}} s_i \Rightarrow^{d_i} \c... |
I have some algorithm and I wonder whether there is a way to optimize it beyond the naive approach.
Basically I have time steps and the current time is $t_c$. At any given time step, a couple of "ranges" are active from now up to some given time $t_i$ (i.e. $\forall t\leq t_i: r_i\in R(t)$).
now -time->
v
r... |
I'm having a hard time with the following question:
Use a recursion tree to determine a good asymptotic upper bound on the recurrence $T(n) = 4T(n/2 + 2) + n$. Use the substitution method to verify your answer.
This is not homework, I'm just practicing myself for an upcoming exam.
The thing I'm having a hard time with ... |
I'm studying support vector machines and came across this paper. The following equation doesn't make sense to me, especially the part with the 0 ∀i. Any help understanding the basics of SVMs?
yi * (xi * w + b) - 1 >= 0 ∀i
xi - one input
yi - the classification (+1 or -1)
w and b - variables to find in order to "trai... |
As big-step operational semantics is about evaluating an expression to a final value, can we state that for defining a concurrent language one needs small-step semantics, as concurrent programs need not result in a value?
|
As there is an untyped lambda calculus, and a simply-typed lambda calculus (as described, for example, in Benjamin Pierce's book Types and Programming Languages), is there a simply-typed combinatory logic?
For example, it would seem that natural types for the combinators S, K, and I would be
S : (a -> b -> c) -> (a -> ... |
I'm a newbie in computer science and would to understand how hardware interrupts work at the physical layer. I ask my question considering a specific example. When packet arrives at the network adapter, a hardware interrupt is raised. Wikipedia says that
an interrupt is a signal to the processor emitted by hardware ... |
As in, I have to design a determenistic (one-taped) turing machine that accepts that language (All strings made up of 0 and 1, where the j-th character from the end is a 0, and $j$ is a constant that we know what it is before running the machine) in less steps than the trivial steps.
In the trivial solution, I would f... |
I'm trying to understand decidable languages. In particular, I would like to show that
$$B = \lbrace \langle D \rangle \mid \exists k \geq 0 \,.\,\text{DFA $D$ accepts $a^k b^k$}\rangle.$$
I don't quite understand the process of proving these. I know that $a^kb^k$ is not regular, so then no DFA accepts it. I also know ... |
I just read about polynomial-size circuit families and I have a question as the title. I know P/poly is defined as the class PSIZE of languages that have polynomial-size circuits. But what about other languages in other classes that have polynomial circuits?
|
I am developing a simple backprop neural network with n inputs and 1 output. I am using a sigmoid activation function. [Aforge.Net]
I have read that it is good to normalise the input and output data prior to training, which I have done using a simple linear relation (max/min mapping) to normalise between [0, 1].
My qu... |
Here is a perhaps naive question that has been tingling me: Is there an $\Omega(\sqrt[3]{n})$ asymptotic lower bound for addressing arbitrarily large memory randomly? My cause of belief is that the shortest path to any memory stored physically must be through three-dimensional space, and the diagonal here must have som... |
This question is inspired by Constructing inequivalent binary matrices.
Define the equivalence relation $\sim$ as follows: If $M,N$ are two $8\times 8$ binary matrices (all elements are $0$ or $1$), say that $M \sim N$ if you can transform $M$ into $N$ by a sequence of moves, where each move picks some pair $(i,j)$ and... |
At 15:30 in this talk (p13 of this presentation here) Rich Hickey mentions the formalisms available for reasoning about Communicating Sequential Processes. He then goes on to mention that these haven't yet been applied to Clojure's core.async.
The only reference I know of for CSP is Hoare's book. I can see some examp... |
I have a problem $A$ which was shown to be PSPACE-complete by reduction from planning.
However, $A$ can also be transformed into reachability problem which is NL-complete.
I know that $NL=NSPACE(log \ n)$ and $PSPACE=NSPACE$.
Does this mean $A$ is also NL-complete? IF yes, does it make any difference in this contex... |
I am reading a unpublished paper describing an algorithm. In one step of the algorithm, there is a bipartite graph $G(X,Y,E)$, where $X=\{1,...,n\}$.
For every subset $X' \subseteq X$, they define
$$f(X')=\bigcup_{i \in X'} \{j \in Y| (i,j)\in E\}.$$
In other words, $f(X')$ is the set of neighbors of vertices in $X'$.
... |
Karp's 21 NP-complete problems show that 0-1 integer linear programming is NP-hard. That is, an integer linear program with binary variables.
If we set the $c^T$ vector of the objective $\text {maximize } c^Tx$ to all one (unweighted, i.e., $c^T=(1,1,\dots,1)$) is the problem still NP-hard?
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For example let's say that we know that the worst-case running time is o(n) and the best-case is o(1). how can i get the average-case running time using the given big Ohs?
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I have several confusion like :
Does virtual address space resides in virtual memory ?
Does each process has its own virtual address space like each process has its own virtual memory and own page table ?
Mapping to physical address takes place from virtual memory or virtual address space if they are different thing ... |
I'm asking here for both the scientific, programmatic, and structural format of a device driver. What does that mean? Basically, I'm not asking how to write a driver in general ... I'm asking how to structure one to behave as software that can act as the "middleware" between higher-level code and the hardware itself. I... |
I've got some questions about the temporal operators in computation tree logic:
Does the Finally path-specific quantifier Fq mean that q has to hold in a subsequent state or is it also fulfilled when q holds in the current state?
Please consider the following example:
What exactly is specified here? Does it mean: If ... |
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