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Nobody yet knows if ${\sf P}={\sf NP}$. Let us consider the following language
$$L = \begin{cases} (0+1)^* & \text{ if ${\sf P}$ = ${\sf NP}$} \\ \emptyset &\text{ otherwise}. \end{cases}$$
A language is said to be recursive if there exists any rule to determine whether a string belong to language or not. We have a rul... |
We may not have a determinate answer to this question. But is there any evidence for or against this question? Or is there any study on it?
|
A file system with 300GByte disk uses a file descriptor with 8 direct block address ,1 indirect block address and 1 doubly indirect block address. The size of each disk block is 128 Bytes and the size of each disk block address is 8 Bytes.What is the maximum possible file size in this filesystem?
This is previous year ... |
Given a list of intervals $[s_1, e_1], [s_2, e_2], \ldots$, what's the most efficient way to determine if an interval $[a, b]$ can be covered by the intervals in the list?
|
I'm trying to separate a weird relationship. It goes like this:
One waiter can serve more than one kind of drink and one kind of drink can be served by more than one waiter.
One waiter can wear more than one kind of shirt (eg different uniforms daily, or random uniform assignments, etc), and one kind of shirt can be w... |
Can anyone explain me what is a trampolined interpreter? I am versed with relevant concepts viz. procedural languages, continuations etc but am finding difficulty understanding the definition/need for trampolining. Please help.
|
When generating a board for Zobrist hashing, why are the initial elements random? How can you detect changes to elements later if the initial values are random?
|
If a set S is infinite and recognizable, how can I prove that, if any, some subsets K is infinite and decidable? how about infinite and recognizable?
|
I have two questions
Is it possible to have 2 languages with different syntax but the same semantics? If not why not else give an example of 2 languages .
Is it possible to have 2 languages with same syntax but different semantics? If not why not else give an example of 2 languages .
I understand that the syntax is the... |
If suppose your hashCode function results in the following hashCodes among others {x , 2x, 3x, 4x, 5x, 6x...}, then all these are going to be clustered in just m number of buckets,
where m = table_length/GreatestCommonFactor(table_length, x)
Can someone help me to prove the above equation.
Example for the above qu... |
Reading this http://classes.soe.ucsc.edu/cmps102/Spring10/lect/17/SAT-3SAT-and-other-red.pdf, I came to know that reducing a clause $C_i$ from a $SAT$ instance containing more than 3 literals to a $3-SAT$ instance is done this way,
Suppose $C_1$ is $\{x_1, x_2, x_3, x_4\}$. It's equivalent representation in 3-literal c... |
I assume the size of an instance of the SAT problem is measured by its number of (Boolean) variables. What is total number of instances of SAT problems of size N?
I guess that amounts to counting the number of "distinct" formulas that can be formed by N boolean variables, using a normal form such as CNF or DNF.
Update... |
Sorry if this is well known, but most of the research is paywalled.
So far I know that it is a subset of the regular languages, but I cannot seem to find any (available) research which pins it down.
Thanks!
|
Can anybody give me an idea how to write this assertion in in first order logic?
X has not passed one or more of the prerequisites for A.
Here, X is the name of a person and A is a constant representing a course name.
|
I am having an AI exam in two weeks, and I am still figuring out certain concepts and ideas, related to Bayesian Nets, Hidden Markov Chains, Conditional Random Fields and Neural Nets (yes it is all going to be tested and yes we have a text (AI - A Modern Approach), but no, we did not cover everything in class).
I "know... |
Is it possible to calculate, efficiently, the minimum tour distance for TSP? That is, the distance without having to provide the actual tour.
If this is not possible (I assume it is not), how tight a lower bound can we efficiently calculate?
|
I drew the map on the right, but what I drew doesn't work for what the question is asking me. I think I did something very wrong, and I don't really understand what this question is asking me. Am i suppose to re arrange the binary inputs somehow?
|
The GSAT (Greedy Satisfiability) algorithm can be used to find a solution to a search problem encoded in CNF. I'm aware that since GSAT is greedy, it is incomplete (which means there would be cases where a solution might exist, but GSAT cannot find it). From the following link, I learned that this can happen when flipp... |
I read that determining the size of the maximum independent set (and also a clique of maximum size) is in P. The versions that find the actual solution are known to be NP-hard.
With respect to finding clique size, you can sort the node degrees, decrement $i$ from $|V|$ to $0$, and each time check if you have $i$ eleme... |
Here is the problem:
Prove that single-tape Turing Machines that cannot write on the portion of the tape containing the input string recognize only regular languages.
My idea is to prove that this particular TM is equivalent to a DFA.
Using this TM to simulate DFA is very straightforward.
However, when I want to use... |
I'm classifying different electrical devices based on features extracted from their electricity consumption into a household-specific model built from around 10 devices. Now I want to detect whether a classified testing instance is coming from a device which has not been present in the training set, i.e. I want to disc... |
In NLP, do you distinguish tokens that you don't observe in a training sample and still expect that they may occur in a test sample, between
those you know what they are, and
those you don't know what they are, and how many of them
If yes, how do you treat them differently to estimate the probabilities in N-grams?
|
Are there dynamic programming examples that run in exponential time? Every example that I've seen so far constructs the top half of a matrix in a bottom-up fashion ($n^2$) from the base case and evaluates $n$ expressions to optimize each entry.
|
I want to prove that a problem $P_1$ is NP-complete. Let say that I want to do a reduction from SAT problem.
If the instance of problem $P_1$ depends on $M$ and $N$, can I specify the sturcture of the instance of the SAT problem?
More precisely, can I say that, for example, the instance of SAT problem is composed of $... |
Given n, I want to randomly generate a binary tree (unlabelled) that has n end nodes. Could someone kindly provide a reference containing an algorithm for doing that?
I attempted to do as follows: From a PRNG obtain n PRNs in [0.0, 1.0) as (relative) frequencies of n symbols for generating a Huffman tree (used in data ... |
If we were to intuitively construct a lower bound for searching an element in a list $A$ containing $n$ integers, it would be in $\Omega(n)$.
But with the decision tree model, the number of leafs is $n$, so we conclude that the lower bound is $\Omega(\log{n})$.
This is the same as finding the maximum element in a list.... |
In the words of (http://www.cs.utah.edu/~suresh/5962/lectures/17.pdf, section 17.2), "Each $f(x)$ can be interpreted as defining a hyperplane in $R^n$. Thus, tracing a path through the tree computes the intersection of the half-planes defined by the nodes touched by the path."
I fail to visualize how path tracing is done... |
I understand what Rice's theorem states and what Trivial and Non-trivial properties mean. However, when given some property, I am having a hard time seeing if it is Trivial or Non-trivial. Can someone help me understand this better, maybe with some good examples?
|
I'm looking for some clarification on some concepts/facts I came across while studying for a class.
I was reading the following wikipedia article. The below specific section and statement intrigued me when looking it over.
http://en.wikipedia.org/wiki/Computational_complexity_theory#Important_complexity_classes
"It tur... |
I am currently developing a math-physics program and I need to calculate if two vectors overlap one another, the one is vertical and the other is horizontral. Is there any fast algorithm to do this because what I came up so far, has a lot of repeats. Eg lets say we have vector V1((0,1),(2,1)) and a V2((1,0),(1,2)) wher... |
I am trying to teach myself complexity. I am trying to come up with a reduction from minimum set cover
(given a set of items $I$, and a set $S$ of subsets of $I$ and an integer $k$, is there a subset $S'$ of $S$ such that $|S'|\leq k$ and $union(S')=I$)
to weighted Steiner tree
(given a graph $G=(V, E)$, a weight fun... |
I am preparing to graduate high school. Although I do not intend to study computer science in college, I feel like it might be useful to familiarize myself with the theoretical CS concepts taught in academia (eg. algorithms, structures, compilers). Can you recommend books that are either frequently used in current CS c... |
Taking this as an example:
bool SolveSudoku(int grid[N][N])
{
int row, col;
// If there is no unassigned location, we are done
if (!FindUnassignedLocation(grid, row, col))
return true; // success!
// consider digits 1 to 9
for (int num = 1; num <= 9; num++)
{
// if looks promisi... |
Let $X_1,\dots,X_n$ be $n$ boolean variables. I have an unknown predicate $P(X_1,\dots,X_n)$ on these boolean variables. Of course, I can view the predicate as a function $f_P : \{0,1\}^n \to \{0,1\}$ that maps a vector of $n$ boolean values to the truth value of this predicate on those inputs.
Now I have a truth tab... |
The principles of calculus, historically, are differentials and integrals [1], while those of algebra are operators and equation solving [2]. Contemporary principles are analysis and abstract objects, respectively.
As an example case, why is relational algebra not called a calculus, and why is the π-calculus not called... |
I have thought about it for a while, and I'm not really sure what is the best way to:
1.Implement a stack using 2 queues.
2.Implement a queue using 2 stacks.
I have only though about something trivial that takes O(n) time for dequeue and enqueue, and O(n) time for push and pop.
Can I do better than that?
Are there mo... |
I'm looking for find the min-cut of a fully-connected directed graph (with cycles), or an undirected graph.
Karger's works but is not guaranteed to produce the correct solution. Is there a guaranteed algorithm?
I came across max-flow algorithms. Do these only work if the graph is acyclic?
Thanks.
|
Suppose I have $N$ bins and $M$ items as depicted in the figure below (3 bins and 3 items):
Suppose that every bin has unit capacity and the weights of the items depend on the bins used. I want to maximize the number of items in the bins subject to:
One bin contains at most one item.
If item $i$ is on bin $j$ then $g_... |
I am a teaching assistant on a course for computer science students where we recently talked about big-O notation. For this course I would like to teach the students a general method for finding the constants $C$ and $k$ in the definition of big-O
$$
|f(x)| \leq C|g(x)|, x > k,
$$
when the function $f(x)$ is a fractio... |
And if so would this grant us any insight into the relations between P, NP, and EXPTIME?
|
I need to write a function that takes in a 2D list, that is a NEARLY magic square, meaning that if you perform ONE swap, it becomes a magic square. The function would take in this nearly magic square, and would return the magic square after the values have been swapped.
I wrote an "isMagic" function already that loops ... |
I have two functions $S$ and $T$ which are interrelated and I want to find the asymptotic worst case runtime. The fact that they are interrelated is stumping me...
How would I find the asymptotic runtime $S(n)$ and $T(n)$?
$$
\begin{align*}
S(n) &= 2S(n/4) + T(n/4) \\
T(n) &= S(n/2) + 2T(n/2)
\end{align*}
$$
|
How many times does the statement count in line 5 executes in terms of $n$?
1. count=0;
2. for (i=1; i<=n; i++) {
3. for (j=1; j<=n; j*=2) {
4. for (k=1; k<=j; k++) {
5. count = count + 1;
6. }
7. }
8. }
For the loop in line 3, we can list the numbers for $j$ as, $2^0,2^1,...,2^{\log n}$
Therefo... |
In section 6.3 of the paper Causal memory: definitions, implementations, and programming, the authors define "data-race free" as follows:
Program $\Pi$ is data-race free if, for all histories $H$ of $\Pi$ and all causality orders $\leadsto$ of $H$, if $H$ has a serialization that respects $\leadsto$ (note that this im... |
While reading Stallings OS Internals and Design, I run into problem. Here is example from the book.
For example, consider a simplified computer in which each instruction occupies one 16-bit word of memory. Assume that the PC is set to the location 300. On succeeding instruction cycles, it will fetch instructions from... |
$$T(n) = 2\cdot \sqrt{n} \cdot T(\sqrt{n}) + \Theta (\lg n)$$
I have been trying to solve this question but I could not find anything.
My approach:
$n = 2^k$
$S(k) = T(2^n)$ and $S(k/2) = T(2^{n/2})$
Finally:
$S(k) = 2^{1+k/2} \cdot S(k/2) + c \cdot \lg(k) $
After that, I tried to build recursion tree but I can not ... |
How will you find a random collection of $n$ points in the plane, all with integer coordinates in a specified range (e.g. -1000 to 1000), such that no 3 of them are on the same line?
The following algorithm eventually works, but seems highly inefficient:
Select $n$ points at random.
Check all $O(n^3)$ triples of point... |
The set of all Turing machines is said to be countable. The central idea of the proof of this fact is that every Turing machine can be written as a finite string of characters. I am having trouble seeing how this could be true.
If we formally define a Turing machine as having a tape language $\{0, 1, \sqcup, x\}$ and i... |
I am trying to find a regular expression and finite automaton that each define $L_1 \cap L_2$, where $L_1 = (ab^*)^*$ and $L_2 = b(a+b)^*$.
How would I start doing this problem?
So I would draw a FA and when I draw it I would have a complement meaning take anywhere you have a plus, get rid of it and anywhere you didn't... |
I have this programming problem, but I really cant figure out what it wants me to do. Heres what it is:
The cube root of a number can be found based on the observation that, if $t$ is an approximation of the cube root of $a$, then $\tfrac13\left(\tfrac{a}{t^2} + 2t\right)$ is a better approximation.
Create a method d... |
This is probably a very basic question but do the polynomials in "polynomial time" have integer, real or complex coefficients?
Everywhere I looked it just says "polynomial expression". I am guessing the polynomial must have integer coefficients?
|
My question is very similar to another solved question. As the title indicates, the major difference in my question is that I need to find the convex polygon that encloses the maximum number of points with a given area (instead of finding the circle that encloses the maximum number of points with a given radius).
So my... |
I'm currently learning untyped $\lambda$-calculus and especially the $\eta$-reduction.
The professor hat the following in his slides:
$$\lambda x. \lambda y. f~z~x~y \stackrel{\eta}{=} \lambda x. f~z~x$$
I don't know how to read and understand this. Could you please explain it to me?
My try
On the left side and the rig... |
I'm not sure what the purpose of the o(1-o) in the back propagation algorithm achieves? I'm guessing it's related to using the sigmoid function on the output but I'd like to have a proper understanding of the math behind it. Thanks!
|
Minimizing deterministic finite automata (DFAs) is a problem that has been thoroughly studied in the literature, and several algorithms have been proposed to solve the following problem:
Given a DFA $\mathscr{A}$, compute a corresponding minimal DFA accepting the same language as $\mathscr{A}$.
Most of these algorithm... |
Given below are 3 different pipelined processors:
$P_1:\ 4\ stages\ with\ delays\ \ \ \ 0.6_{ms}\ \ 0.8_{ms}\ \ 0.6_{ms}\ \ 1.1_{ms}\\
P_2:\ 4\ stages\ with\ delays\ \ \ \ 2.0_{ms}\ \ 1.8_{ms}\ \ 2.0_{ms}\ \ 1.0_{ms}\\
P_3:\ 5\ stages\ with\ delays\ \ \ \ 1.0_{ms}\ \ 0.8_{ms}\ \ 1.0_{ms}\ \ 1.5_{ms}\ \ 1.5_{ms}$
One ha... |
How to display distinct rows from single column without using DISTINCT keyword and [having count(*) > 1 ] ? My question is can we do this using sub-queries or co-related sub query ?
If yes how we can do this ?
Please let me know.
Thanks.
|
I'm taking a graduate computer science course on algorithms and analysis. The current subject is big O notation and recursion. How is the following problem related to the study of algorithms, recursion, and big O notation? I know and understand the solution to the problem, but I just don't see how this is relevant to t... |
Suppose you have an NP problem, and a polynomial time verifier which accepts valid solutions within $f(n)$ operations.
You make a tweak to the verifier program, so that if it takes more than $f(n)$ operations, it unconditionally rejects. Then you place it into an NP machine and run it on all possible certificates for s... |
How can we add new words to DFA, maintaining minimality?
Maybe, you can advise some completely different approach to solve the following problem:
A program must process two types of queries:
Add new word to the language.
Check if some word of the language occurs in the input string as a substring.
Time and space com... |
I've written a genetic algorithm (GA) that solves a 7-dimensional optimisation problem. All seven variables are floating point numbers. The problem is that the entire population seems to converge to very nearly the same point in the solution space within about 20 generations, even if I increase the population size by... |
I am new to machine learning, so forgive me if I am doing something absolutely absurd.
I have a classification task (~100 classes) and have about 2 million training data points in a 2000-dimensional space. Coordinates of data points are integers (discrete). All points have non-zero coordinates only for < 10 dimensions.... |
In his famous Semantical Analysis of Intuitionistic Logic,
S. Kripke speaks of the "well-known mappings of intuitionistic logic
into the modal system S4". I'm not sure which mappings Kripke means.
One guess would be K. Gödel's "Eine Interpretation des
Intuitionistischen Aussagenkalküls" (translated into English as "An
... |
In section 17.4.5 "Happens-before Order" of Java Language Specification, a trace is examined for the notion of happens-before consistency.
The trace is shown in the figure in which $A$ and $B$ are shared variables with initially $A = B = 0$.
An execution order of the trace is as follows.
In this execution, the rea... |
I remember a riddle about a bunch of people on a river bank, and a boat with limited capacity (lets say the boat can transport 2 people at a time). There are various relations between the people like: person $x_m$ and $x_n$ cannot sail together and cannot even stay on the same bank of the river or $x_m$ and $x_n$ alway... |
I am currently reading Introduction to the Theory of Computation (Sipser), and after introducing epsilon labeled transition arrows, the book shows the following NFA:
I was following it until I read the following :
Practice with it to satisfy yourself that it accepts the strings ϵ, a, baba and baa...
What does an inp... |
Why functional programming languages do not use Von-Neumann architecture?Please explain elaborately.It'll be more helpful if you explain it diagrammatically. Thanks in advance. :)
|
It is well known that 3-SAT is $\sf NP$-complete , but 2-SAT is in $\sf P$. Let there be a formula with $n-1$ clauses with 2 literals each and only 1 clause with 3 literals.
We can solve this case in polynomial time, separating and solving in a brute force manner the 3 literal clause and then for each satisfying as... |
Lets say that I am storing 10^9 keys in a single BST.
Compared to having lets say having multiple BSTs of sizes 10^6 containing chunk of the bigger tree? Search through all of them executing in parallel.
I am talking about only search performance here, Given that processing power is not a bottle neck.
|
I want to show that some problem $P_1$ is NP-hard. I have a problem $P_2$ that is NP-complete. From an instance of $P_2$ I created in polynomial time an instance of the problem $P_1$.
My question is: Should I verify both direction ($\Leftrightarrow$) or only one direction ($\Rightarrow$)? More precisely, which one to s... |
Has anyone ever actually written a system (software or detailed explanation on paper with simple examples) that generates computer programs? I input $Prime(x) \wedge x<10$ and it creates a program that lists the prime numbers less than 10. $Prime(x)$ is simply defined as
$$1<x \wedge \not\exists A\; s.t. 1<A \wedge ... |
I'm studying for my exam and I came across the following exam question from last year, the only way I know how to solve this is build a regex that accounts for all six different series of letters so for example to recognize a string that has the letters a,b and c occur in that order:
$(a+b+c)^*a(a+b+c)^*b(a+b+c)^*c$
Th... |
Given a graph $G=(V,E)$ and a set of colors $k<V$. Find a assignment of colors to vertices that minimizes the number of adjacent vertices in conflict. (Two adjacent vertices are in conflict if they have the same color.)
I want to prove the above problem is NP-complete. Call the above problem P1.
Answer: I am trying to ... |
Suppose we have two language
L = {0^n|n>=0}
M = {1^n|n>=0}
We know both of these are regular languages.
Will L.M (concatenation) be a regular language? Please explain your answer and if yes then what will be its expression?
Thanks for any help in advance.
Adding to it, we know that language {o^n1^n|n>=0} isn't a regul... |
Lets say you have a data model that consists of a 2D grid of integer points. This grid is sparsely populated and boundless in x and y (up to the max of a 32-bit integer).
What is the best way to index these points in order to have an optimised lookup on an arbitrary (x,y) coordinate? Is an O(1) lookup solution possible... |
I was working on recurrence relation and came across this example
T(n) = 2T(n/2) + log(n)
What will be the time complexity, ie, big O for this relation.
Thanks for any help in advance.
|
I began a chapter in a textbook on computational theory where they begin to talk about decidable languages.
The problems in this section are pretty confusing and I honestly don't know how to begin them because I'm not 100% on what they mean when they say "countable".
Can anyone help walk me through this problem in th... |
Consider a set of $N$ nodes. There is a $N\times N$ non-negative valued matrix $D$ where the $(i,j)$th element $d_{ij}$ gives the "positive metric" between node $i$ and $j$, where $i,j\in [N]$. Thus the diagonal entries of $D$ are all zero and $d_{ij}=d_{ji}$ so $D$ is symmetric.
Then there is a set of $k$ colors. I ... |
I have the following homework question that I am struggling with. I have read the corresponding chapter from the book, but no guidance there.
Consider a linked list $X: X_1 \to X_2 \to X_3 \ldots$.
Assume that the cost of examining a particular element $X_i$ is $C_i$. Note that to examine $X_i$,
one needs to scan thro... |
Is there any literature about the complexity of the integer knapsack problem with bounded weights? To make it clear, I want an optimal solution to the following problem:
$\max \sum_{i=1}^k c_i \cdot x_i$
$\sum_{i=1}^k w_i \cdot x_i \leq W$
$x_i \in \{0,\ldots,k_i\}$
where $k_i$ is an item-specific limit for the number ... |
Is there a non-regular language over unary alphabet $\{a\}$ which has a Myhill-Nerode equivalence class that is not a singleton?
|
I have a table of pairs of objects, which defines an equivalence relation. How can I extract a single object from each of the equivalence classes using relational algebra?
It can easily be done with iteration. For example, associate a unique classId with every object, then for every pair (a, b) set classId(a) = classId... |
I have a sphere (radius R) on a rectilinear grid. Some cells intersect the edge of that sphere, call them 'edge cells'. Designate a given cell by indices [i,j,k] which refer to the lowest-index vertex of that cell (i.e. the inner-most cell, in the [+x,+y,+z] octant would be designated as [0,0,0]). For any given 'edge c... |
Basically, I using an algorithm called 'miranda' to look at miRNA targets and it only runs on a single thread. It compares everything in one file against everything in another file, produces a file as an output and runs off of the command line in terminal. The process took roughly 20 hours to create the output file.
I ... |
I'm reading up on propositional logic, and I'm completely stuck on this example - spent the past few hours trying to figure it out! Any pointers would be appreciated.
There's 2 trees, each with signs on.
Sign 1/Tree 1: There are leaves on this tree, and no leaves on the other
Sign 2/Tree 2: There are leaves on one of ... |
I understand the basis of A* as being a derivative of Dijkstra, however, I recently found out about D*. From Wikipedia, I can understand the algorithm. What I do not understand is why I would use D* over Dijkstra. To my understanding, Dijkstra gives a best path and D* works backwards from the end goal, but unlike A* it... |
I'm going over some of the pre-requisite math regarding Automata theory, and finite representations.
I read the following:
If ∑ is a finite alphabet the set of all strings over the alphabet
(∑*) is countably infinite.
The set of all possible languages over an alphabet ∑ is uncountably
infinite.
How can the set of lan... |
I have few CS textbooks with me which discuss languages, well actually 2 plus old course notes supplied a few years ago. I have been searching the web too any only seem to come up with vague responses just like the text books I have.
My question is about language recognizers verses generators.
I get the overriding pri... |
I have been working on a challenge i found on the internet. It is as follows:
You've stumbled onto a significant vulnerability in a commonly used cryptographic library. It turns out that the random number generator it uses frequently produces the same primes when it is generating keys.
Exploit this knowledge to factor... |
I'm having trouble thinking about the following. If we have two machines 1 and 2 that evenly split a set of data points, does $k$-means separately, then averages the result, does this agree with just $k$-means on one machine?
To be more specific, consider the following routine:
Split an input dataset evenly between 1... |
Having large matrices, $W$ (the unknown) and $M$ (known), is it possible to solve for $W$ in this equation
$$W \cdot W^{T} = M,$$
where $M$ can have negative entries.
|
For a regular array, I understand that if we have the tradeoff of space vs time, and we use more space to implement a Which, Data, and When pointers to the actual array, we can initialize the array in constant time because there are pointers to access and keep track of the elements in the array.
How can I extend the id... |
I read in these two papers http://www.ccs.neu.edu/home/lieber/courses/csg260/f06/materials/papers/max-sat/p216-schaefer.pdf and http://people.csail.mit.edu/madhu/papers/noneed/fullbook.ps that if we have a boolean formula that is $0-valid$ then (of course) SAT problem is in $\mathcal{P}$ but finding a solution with max... |
I am a high school student in the twelfth grade. I study high-level programming, and a little bit of basic computer science.
I have recently started to understand what a Turing Machine is. I wanted to ask:
I understand that a Turing Machine is a hypothetical device used to explain the mechanisms of computing.
But is a ... |
I am a senior year high school student. I love programming and my chosen language is Java. I'm very much into high-level programming and Object Oriented design.
Recently, I started to show first interest in the low-level side of things. Especially the most basic level of how computers work (the more theoretical level, ... |
I have a cost function $f(X)=\|\hat{X}-X\|_2$ to minimize which depends on a $s\times s$ matrix $X$ where $\hat{X}$ is given and $\|X\|_2=\big(\sum_{i,j}x_{ij}^2\big)^{1/2} $. This matrix $X$ is generated by selecting only $s$ different rows from a matrix $B$ of dimension $n\times s$. At the end, we are going to choose... |
If my goal were to compress say 10,000 images and I could include a dictionary or some sort of common database that the compressed data for each image would reference, could I use a large dictionary shared by the entire catalog and therefore get much smaller file sizes? Could this be expanded to work with images in ge... |
Sorry this is a basic question to understand decidability. It is the first time I see it in my undergrad course.
1)
I am reading why the language AFDA is decidable and why ATM (halting problem) is not. The explanation says that the emulated TM in ATM might loop forever. I agree, because a specific input string might ma... |
I've implemented a program for computing eigenvectors of some random, symmetric, $N$x$N$ matrix using the power method. I have found difficulty in calculating all $N$ eigenvectors consistently, almost every time the algorithm fails to converge for all $N$. The Wikipedia page on the power method tells me this algorith... |
Let an integer n be given. Write the integers from 1 to n in binary notation successively from left to right. In the resulting string consisting of zeros and ones, choose a palindrome substring of maximal length. It is required to find the length of this substring. For example, if n=5, we can get a string which is 1 10... |
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