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I have been using Harwell Boeing format, also known as Compressed Column Strorage (CCS) in order to store Sparse Matrices.
Could you please suggest me some other way to store/represent sparse matrices?
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Hi I've read this lemma in my book:
Lemma 2.1. Let $p(n) = \sum_{i=0}^{k} a_in^i$ denote any polynomial and assume $a_k > 0$. Then $p(n) \in \Theta(n^k)$
Proof. It suffices to show that $p(n) \in O(n^k)$ and $p(n) \in \Omega(n^k)$. First observe that for $n > 0$,
$$p(n) \leq \sum_{i=0}^{k} |a_i|n^i \leq n^k \sum_{i... |
I have a function which takes 22 real-valued parameters as input that returns a real value. The function is reasonably fast for low return values (ms/seconds/minutes), but takes much longer (minutes/hours) to compute for high/optimal values. The noise will also increase with higher values.
I expect the function to cont... |
In the Hopcroft-Karp algorithm for bipartite matching, I don't understand the purpose of the breadth first search. I think it's used to find a set of vertex disjoint augmenting paths, but I'm not sure what the significance of that is or even what that means. Why do the augmenting paths have to be the shortest? And w... |
The MAX k-SAT problem is:
“Given a set of clauses C1,…,Ck, each of length k, over a set of
variables x1,…,xn, find a truth assignment that satisfies as many of
the clauses as possible.”
I'm trying for find a randomized 0.999-approximation algorithm for the MAX 10-SAT problem. Help :(
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Given a directed graph with the following attributes: - a chain from node $a$ to node $z$ passing nodes $b$ to $y$ exists and is unidirectional. - additionally a set of nodes having bidirectional vertices to at least two of the nodes $a \ldots z$ exists. These nodes are connected in a second unidirectional chain.
(the... |
Given two strings $x$ and $y$ over the alphabet $\{A,C,G,T\}$, I'm trying to determine a shortest string $z$ such that $z$ is a subsequence of $x$ and not a subsequence of $y$.
Example: a shortest string that is a subsequence of AATGAAC but not a subsequence of ATCGATC is AAG.
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Consider the following Google Code Jam round 1C question:
The Great Wall of China starts out as an infinite line, where the height at all locations is $0$.
Some number of tribes $N$, $N \le 1000$, will attack the wall the wall according to the following parameters - a start day, $D$, a start strength $S$, a start west-... |
So basically L satisfies the conditions of the pumping lemma for CFL's but is not a CFL (that is possible according to the definition of the lemma).
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There is a famous Consensus Problem in Distributed Computing.
Let's consider and try to find the best possible algorithm for a simplified version of the consensus problem.
Assumptions: a process may undergo only crash failure (process abruptly stops and does not resume), process represent a complete graph.
Simplificat... |
Given three strings $x$, $y$, and $z$ over an arbitrary finite alphabet, I need to determine their longest common subsequence (LCS).
Example: A longest common subsequence of bandana, cabana, and magazine is aan.
I'm trying to find an algorithm which uses $O(|x|\cdot |y| \cdot |z|)$ space where $|s|$ denotes the length ... |
In Coq, you can use two different kinds of keywords to do definitions--Inductive and Definition. I do not understand the difference between an inductive and a definition, or when it is appropriate to use one instead of the other.
Could someone with experience in Coq please shed some light on this, or provide a referen... |
I'm trying to find an efficient method of detecting whether a given graph G has two different minimal spanning trees. I'm also trying to find a method to check whether it has 3 different minimal spanning trees. The naive solution that I've though about is running Kruskal's algorithm once and finding the total weight of... |
The wikipedia article about primitive recursion states that
An equivalent definition states that a partial recursive function is one that can be computed by a Turing machine.
My question is how one can write down formally this definition?
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I've designed a few databases in my time, and on more than one occasion the drive to abstract common elements from specific tables has led me to create generic top-level tables which contain those common elements. For example:
Table Column Column
Hamburgers Item Topping
Cheeseburger ... |
This question stems from a few answers and comments on a question I posted in signal processing found here.
I guess I am a little confused. Are there any concrete differences between realtime software/hardware and just a regular PC?
I would try to list what I think the differences are but the list I have come up with ... |
I am trying to (intuitively) understand the two terms "decidability" and "verifiability".
I have done a reasonable amount of searching and going through the various texts I can put my hands on. However, their intuitive understanding seems to escape me, specially for the second one.
Out of the many definitions found, th... |
If I am correct, chips cannot get much smaller because of Heisenberg's uncertainty principle. My friend and I want to perform an experiment (which is cheap, i.e. doesn't require million-dollar equipment) which shows that if a chip is too small, it will mess up. Is there any such experiment?
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I wonder how it's possible that:
it can be shown that all reasonable choices of programming
languages lead to quantification of the amount of absolute information in
individual objects that is invariant up to an additive constant.
from the Preface to the First Edition, An Introduction to Kolmogorov Complexity ... |
I am having trouble trying to formulate a simple proof. I can clearly see that what I am trying to prove is correct but to prove it I am not sure what to do.
The problem is a broadcasting problem on a graph. My graph contains two cycles. The two cycles are joined by a single vertex $v$. If the vertex $v$ contains some ... |
This is more of an open-ended information question, but to make it concrete, here's an example problem I have thought up:
Consider an $N\times N$ grid, $N$ odd, and consider that a single chunk of rare, valuable metal, lies buried under one of the unit squares with uniform probability.
An agent, $X$, starts at the cent... |
What I want to do is turn a math problem I have into a boolean satisfiability problem (SAT) and then solve it using a SAT Solver. I wonder if someone knows a manual, guide or anything that will help me convert my problem to a SAT instance.
Also, I want to solve this in a better than exponential time. I hope a SAT Solv... |
So, I have a book here, which has an example for context sensitive grammar, and the grammar is the famous $0^n1^n2^n$ , and it has:
$$ \begin{align}
S &\rightarrow 0BS2 \mid 012 \\
B0 &\rightarrow 0B \\
B1 &\rightarrow 11 \\
\end{align} $$
I agree that the above works, but what is wrong with just saying:
$S\rightarrow... |
This is something I've been wondering for years. Software like Mathematica is great at manipulating expressions into simplified, factorized, and other forms. I'm wondering if there's a way, theoretically and/or practically, to find the form that has the fewest operations. The next step would be to prefer operations tha... |
For example, if n=14, the output should be 10; n=22, the output should be 30=10+20; n=102, output=(10+...+100)+101+102=5703
In this problem, n is smaller than $10^{18}$ , and the algorithm should finish within 1 second.
|
Is it proper to view conditional probabilities, such as the forms:
P(a|c)
P(a|c,d)
P(a, b|c, d)
...and so forth, as being tensors?
If so, does anyone know of a decent introductory text (online tutorial, workshop paper, book, etc) which develops tensors in that sense for computer scientists/machine learning practitioner... |
I have an integer linear program (ILP) with some variables $x_i$ that are intended to represent boolean values. The $x_i$'s are constrained to be integers and to hold either 0 or 1 ($0 \le x_i \le 1$).
I want to express boolean operations on these 0/1-valued variables, using linear constraints. How can I do this?
Mor... |
What i actually want to do is to turn a math problem ,i have to solve,to a Boolean Satisfiability problem and solve it using a SAT Solver.
I wonder if someone knows any manual,guide or anything that will help me to make my problem solve using a SAT Solver.From what i found so far,SAT Solver's do not have any good docum... |
Can someone explain me how to find if these formulas are equivalent with Kripke structures?
AG(Fp or Fq) , A(GFp or GFq)
AGF(p and q) , A(GFp and GFq)
AFG(p and q) , A(FGp and FGq)
Thank you in advance for your help :)
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I have recently been asked in an interview to devise an algorithm that divides a set of points in a coordinate system so that half of the points lie on one side of the line, and the rest on the other side.
The points are unevenly placed and the line must not pass through any of the points.
Can any one give any approach... |
I have a question about the structure of the complexity class $APX$. Obviously, unless $P=NP$, no problem in the class $PTAS$ can be $APX$-complete (under the AP-reduction). However, what about the rest of problems in $APX$? Are there any problems known that are in $APX$, do not have a $PTAS$ (unless $P=NP$) and at the... |
I'm taking a grad level randomized algorithms course in the fall. The professor is known for being very detail oriented and mathematically rigorous, so I will be required to have an in-depth understanding of probability. What would be a good probability book to learn from that would be intuitive, but also have some mat... |
Let $G = (V,E)$ be a directed graph with a weight function $w$ such that there are no negative-weight cycles, and let $v \in V$ be a vertex such that there is a path from $v$ to every other vertex. Let $f : V \to \mathbb R$ be a given function. Describe an algorithm that runs in $O(|V| + |E|)$ time that answers yes/no... |
Can someone suggest an algorithm to solve job assignment problem with condition?
With condition means that some jobs cannot be done by some workers. For example table as shown below:
In this table x - means that it is impossible to do. For example, worker 1 cannot do jobs 1,3 and 5.
I encountered such situation and th... |
I've ran some tests and found that Shellsort runs much faster on ordered and reversed lists compared to random lists and almost ordered lists.
Results:
Random Reverse Order AlmostOrder
time 24 5 4 29
The problem that is confusing me is that Shellsort performs insertion sorts on lists sepa... |
We have some programs in a very basic imperative language, the programs contain some basic features: assignment, condition, loop, scalar variables, 1-dimensional arrays and 2-dimensional arrays... Note that a variable or an array may not be initialized (or already hold a value before the execution of a program).
My que... |
I wrote a program which implements Bellman-Ford, and identifies when negative weight cycles are present in a graph. However what I'm actually interested in, is given some starting vertex and a graph, which path do I actually trace to get to the original vertex having traveled a negative amount.
So to be clear say I ha... |
I want to know what is algorithm and time complexity of Hanoi tower with forbidden direct move from source to destination (it means you cannot move disk from source to destination directly and you instead of that should first move disk from source to middle and then from middle to destination) and other rules as normal... |
I was wondering. May the source and sink have in-out going edges in a flow-network, and if so - does Ford-Fulkerson and the max-flow min-cut theorem apply ?
Flow-networks are always pictures with no edges entering source, and no edges leaving sink.
I've tried to search the web for an answer, but did not come across an ... |
As a continuation of my previous question i will try to explain my problem and how i am trying to convert my algorithm to a problem that can be expressed in a CNF form.
Problem: Find all stable sets of an argumentation framework according to Dung's proposed framework.
Brief theory: Having an argumentation framework AF,... |
I'm a Computer Science student and am currently enrolled in System Simulation & Modelling course. It involves dealing with everyday systems around us and simulating them in different scenarios by generating random numbers in different distributional curves, like IID, Gaussian etc. for instance. I've been working on the... |
I was wondering when languages which contained the same number of instances of two substrings would be regular. I know that the language containing equal number of 1s and 0s is not regular, but is a language such as $L$, where $L$ = $\{ w \mid$ number of instances of the substring "001" equals the number of instances o... |
This might be a bit of an abstruse question, but it's something I've been trying to prove.
I'm trying to show that it is undecidable whether a given Turing Machine is a member of the set of all Turing Machines that either always halt, or have non-halting loops where all of which can be detected (a positive decision mad... |
I am trying to estimate the graph in very high dimensional data, I mean with million nodes. Up to now all the papers that I have found, they are limited to few thousands.
All of them like graphical lasso, non parnormal, they use the estimated covariance matrix and then use the gaussian likelihood function which they op... |
Some authors define $\Omega$ in a slightly different way: let’s use
$ \overset{\infty}{\Omega}$
(read “omega infinity”) for this alternative definition. We say that $f(n) = \overset{\infty}{\Omega}(g(n))$
if there exists a positive constant $c$ such that $f(n) \geq c\cdot g(n) \geq 0$ for infinitely many integers $n... |
Is the following problem NP-complete? (I assume yes).
Input: $k \in \mathbb{N},G=(V,E)$ an undirected graph where the edge set can be decomposed into two edge-disjoint simple cycles (these are not a part of the input).
Question: Is there a simple cycle in $G$ with length greater than $k$?
Obviously the problem is in ... |
The rules I am considering are $\frac{\neg A, \ \Gamma \implies \Delta}{\Gamma \implies \Delta, \ A} (\neg L)$ and $\frac{\Gamma \implies \Delta, \ \neg A}{A, \ \Gamma \implies \Delta} (\neg R)$
I am trying to get my head around some of the sequent calculus rules, and while I think I understand most of them, I am strug... |
Let G be a directed graph with non-negative weights. We call a path between two vertices an "odd path" if its weight is odd.
We are looking for an algorithm for finding the weight of the shortest odd path between any two vertices in the graph.
If possible, describe one algorithm that is reduction-based (that is, make s... |
So I'm learning about distributed computing, and I do understand a lot of the prerequisite material on algorithms and automata and whatnot... but I'm curious about the definitions I'm seeing as I read my textbook.
A system consists of $n$ processors $p_{0},\dots,p_{n-1}$, where $i$ is the index of the processor $p_i$.... |
$$T(n) = 2T(n/2) + \Theta(n), n > 1$$
$$T(n) = \Theta (1), n \le 1$$
$$G(n) = G(\lfloor n/2 \rfloor) + G (\lceil n/2 \rceil) + \Theta(n), n > 1$$
$$G(n) = \Theta (1), n \le 1$$
Prove $T(n)$ and $G(n)$ have the same asymtotic running time.
I tried using the sandwich theorem but got nowhere. Please be really explicit and... |
I have recently learned about various randomized algorithms for load balancing. The model is always that there are $m$ balls and $n$ bins and the balls arrive one at a time. The task is to minimize the maximum load of any bin. However there is something I don't understand.
Why not just keep a priority queue of the loa... |
Can the set of states Q be empty by definition?
I was wondering about this question when doing exercises in the pumping lemma for finite automaton.
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If A many-one reduces to B, does the complement of A many-one reduce to the complement of B? My gut says no but I am having a hard time finding a counterexample.
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Image on the top is in the time domain, image on the bottom is in the frequency domain.
Why do we see -2T and 2T on image of the time domain and why do we see -1/2T and 1/2T of the image in the frequency domain?
|
There is a greedy algorithm for finding minimum vertex cover of a tree which uses DFS traversal.
For each leaf of the tree, select its parent (i.e. its parent is in minimum vertex cover).
For each internal node:
if any of its children is not selected, then select this node.
How do I prove that this greedy strategy g... |
Exactly as stated in the subject. I look for grammar which use letters $a, b ,c$ that numbers of letters $c$ is greater than number of letters $b$.
Example: $acbccba$ is generated by the grammar.
I thought about:
$S \rightarrow aS \mid bS \mid SCS$
$ C \rightarrow cb \mid ca$
but not sure if it works. Could you help me... |
[Input]: the begin and end points of an arbitrary line (small red points) and the line width (green line)
[Example]: begin=(20,20), end=(100,50), width=5
[Output]: The set of pixels (not the total area) that are in the yellow rectangle
[Example]: {(20,20), (20,21), (20,22),...etc.}
How can i calculate the output set?
|
I'm facing some problems that deal with finding common elements between unsorted arrays and I'd like to know whether there are well-known lower-bounds for the worst-case and, eventually, what are these lower-bounds.
The problems are pretty simple:
Given two unsorted arrays of distinct integers, $A$ and $B$, of size
... |
i'm going to use the Christofides heuristic algorithm in order to solve a TSP for about 80 edges. Eventually i should have a solution, that is within the factor 1.5 of the optimum.
But when i'm finished, i'd like to check my solution but i don't know how. So i thought about using a computer-program to find the optimal ... |
I look for grammar which use letters $a,b,c$ that numbers of letters $c$ is greater than number of letters $b$.
Example: $acbccba$
I thought about:
$$S \rightarrow aS \mid bS \mid SCS$$
$$C \rightarrow cb \mid ca$$
but not sure if it work. Could you help me, please.
|
I've seen two definitions of a universal hash family, and my questions is if those are equivalent, i think they are and will explain why but i'm not sure if it is.
Definition 1:
$H$ is a universal hash family if and only if $$\mathbb{Pr_{h \in H}}[h(k) = h(l)] = 1/m$$
where $k \neq l$ and $k,l\in Key$ and $m$ is the Si... |
I am new in complexity theory and this question is a part of a homework that I have and I am stuck on it.
Let ${\sf coNP}$ be the class of languages $\{\overline{L}: L \in {\sf NP} \}$.
Show that if ${\sf NP} \neq {\sf coNP}$, then ${\sf P}\neq {\sf NP}$.
|
How to prove that the largest number of leaves in an $n$-tree of height $k$ is $k^n$?
|
I've been recently studying Monte-Carlo and other randomized methods for a lot of applications, and one that popped into my mind was making an (approximate) convex hull by examining random points, and try to get them inside the convex hull. I would like to know if there are algorithms for convex hulls that can improve ... |
I am having trouble with a past exam paper. I have to design a Turing Machine to do the following, but I don't really know where to start with this question. Any help would be very much appreciated.
Design a Turing Machine TM checking if the numbers of sold apples and bananas are even. Formally, given a string w over ... |
Given a set of rectangles, $D = \{ (a_1, b_1), (a_2, b_2) \dots , (a_n, b_n) \}$, where in each pair $(a_i, b_i)$, $a_i$ represents the height of the rectangle and $b_i$ the width, and given another pair $(w, h)$ representing the width and height of a container $C$, does exist a way that taking some of the squares in $... |
I am reading two books, Computer organization and design by David A Patterson, and Digital Design and Computer Architecture by Harris and Harris. These books claim that a 1 bit branch predictor mispredicts on the first and last iterations of every loop.
I don't understand why it mispredicts on the first iteration. I th... |
I'm fairly new to the syntax of relational algebra, and I'm having a hard time understanding how I could set a "at least one" clause.
Example: I have:
a table with books (listing the title, year published and ID),
a table with authors (listing their name and ID),
a table which lists what author wrote what book (thro... |
Here's the problem:
I have a collection of collections, $C$, where each $c\in C$ is a collection of sets $X\subset U$. Denote $c_i$ as the i-th $X$ in $c$. Informally, I want to map all the sets in each collection to bins, where no two sets in a single collection can occupy the same bin, such that the sum of the size... |
How can I deal with recursive terminals in CFG when converting it to CNF? For example,
S -> MN
M -> AM | A
N -> BN | B
A -> a
B -> b
How can I reduce terminals M and N?
|
Radix sort is theoretically very fast when you know that the keys are in a certain limited range, say $n$ values in the range $[0\dots n^k -1]$ for example. If $k<\lg n$ you just convert the values to base $n$ which takes $\Theta(n)$ time, do a base $n$ radix sort and then convert back to your original base for an ove... |
Let $\mathbb{F}^n_2$ denote the set of $n$-bit 0-1 strings. How to construct an efficiently computable function $f:\mathbb{F}^n_2\to \mathbb{F}^m_2 (m>n)$ satisfying that $\forall u\neq v$,$f(u)\neq f(v)$ and $f(u)$ is not a circular rotation of $f(v)$?
$m$ is expected to be as small as possible.
Thank you very much fo... |
May be it's a stupid question (sorry if it's the case).
What is the complexity the decision problem:
Input: $A\in\mathcal{M}_{n,m}(\mathbb{Z})$
does there exists $x\in\mathbb{N}^n,x>0$ such that $Ax\geq 0$?
Where $x\geq 0$ means for all $x_i\geq 0$ and $x>0$ means there exists $x_j>0$.
I know that integer linear progra... |
Consider the following universe problem.
The universe problem. Given a finite set $\Sigma$ for a class of languages, and an automaton accepting the language $L$, decide if $L=\Sigma^*$.
In [1], it is stated and proved that the universe problem is undecidable for a particular class of one-counter automata. This result... |
What's the difference between a stream and a queue? They both have the concept of an ordered set of elements, but tend to have different implementations and a different vocabulary of 'insert'/'extract' (streams) vs. 'enqueue'/'dequeue' (queue). Are these interchangable? Do they suggest different concepts or patterns? I... |
This was a question at SO, and I think it's very interesting, I thought about it, but I could not provide any efficient algorithm neither showing the NP-Hardness:
Find the length of the longest non-decreasing sequence through
adjacent, non-repeating cells (including diagonals). For example, in the
following grid, ... |
Given a weighted digraph, I can check whether a given vertex belongs to a negative cycle in $O(|V|\cdot|E|)$ using Bellman-Ford. But what if I need to find all vertices on negative cycles? Is there a way to do it faster than Floyd-Warshall's $O(|V|^3)$?
|
It is clear that any language in $\mathsf{EXP}^{\mathsf{EXP}}$ can be computed in $\mathsf{2EXP} = \mathsf{DTime}(2^{2^{\mathsf{poly}(n)}})$.
My question is whether the converse is true: is $\mathsf{2EXP} \subseteq \mathsf{EXP}^{\mathsf{EXP}}$?
|
I'm trying to find two languages, $L_1, L_2 \in RE \setminus R$, such that $L_1 \cup L_2 \in R$.
I have already proved that if $L_1\cap L_2 \in R$ and $L_1 \cup L_2 \in R$, such $L_1, L_2$ don't exist (because otherwise we'll be able to construct a Turing Machine $M_1$ which will decide $L_1$, for instance).
However, I... |
What I have
An iterative process based on the application of a very simple function to represent a rate, with total dependence among any iteration and its predecessor (one input parameter for (n)th iteration is the output parameter from the (n-1)th iteration). Specifically,
$\qquad f(x, y, z) = x + \frac{y - x}{z + 1}... |
Question:The set of all first names given to children born in New Zealand in 1996
I think this language is regular because every element in the set can be a accept state
How can I prove if the language is regular?
|
I am reading an article called The temporal semantics of concurrent programs
.
On page $9$, there is a small section (numbered as $2$) called "clean behavior".
I think that there is a problem with this part, what does Pnueli meant by "Let $\lambda_i$ be the leagality condition for the statement departing from $m^i$" ?
... |
Input: A set of $n$ Users $U=\{u_1, ..., u_n\}$ and a set of $m$ products $I=\{i_1, ..., i_m\}$. Associated with each pair $u \in U$ and $i \in I$ is the probability $p_{u,i}$ of $u$ purchasing the product $i$.
Task: Assign each user exactly $k$ products so that the following objective function is maximized:
$$\sum... |
BB(n) is roughly the maximum number of new states an n-state TM can run into without halting. So for a particular n, if we know BB(n), then we can find out if an arbitrary n-state TM halts by running it for BB(n) steps.
So given some n-state TM, can we construct an m-state TM, where m>n, to calculate BB(n) and thus dec... |
Given a PDA $P=(Q,\sum,\delta,q_0,F)$ construct formally a TM that accepts $L(P)$.
My idea is to construct a Turing machine with 2 tapes, one for the input and the other for the stack. Also to add $q_a$ for accept and $q_r$ for reject and to send to $q_a$ if the TM stops on states in $F$ and send to $q_r$ otherwise.
Bu... |
Given two arbitrary regular expressions, is there an "efficient" algorithm to determine whether they match the same set of strings?
More generally, can we compute the size of the intersection of the two match sets?
What algorithms are there to do this, and what complexity class do they live in?
If we disallow the Kleen... |
I need a little help with a lambda calculus reduction to normal form:
$$(\lambda xxxx.xx)(\lambda x.xx)(\lambda x.x)y((\lambda x.x)x)$$
It should be solved like this:
$$xx(\lambda x.x)y((\lambda x.x)x)$$
and then:
$$xx(\lambda x.x)y(x)$$
This is the result of any of the lambda calculators that you can find online.
My q... |
Here is my problem. I have to compute the amount of information that is possible to encode in a string of bits. This string of bits represent a stream.
Let us call such stream as $X_1,X_2,X_3,...,X_n$. Important: this succession of Random variable is not a Markov Process, but a process with memory!!
I suppose that the ... |
The government wants to create a team with one alchemist, one builder, and one computer-scientist.
In order to have good cooperation, it is important that the 3 team-members like each other.
Therefore, the government gathers $k$ candidates of each profession, and creates their "liking" graph. This is a tri-partite gr... |
I'm studying the PCP theorem.
While it is easy to prove that $\mathsf{P}=\text{PCP}(O(\log n),0)$ , proving that $\text{PCP}(O(\log n),1)\subseteq \mathsf{P}$ i.e. PCP that uses $O(\log n)$ random bits and read 1 bit of the proof is less obvious, what I tried to do is to take some proof $\pi$ of length $n^{O(1)}$ (be... |
Let,
game be the state of a 2-player, turn based game
actions game player -> [move] be a function that gets the state of a game and returns all valid moves, where a move if a function move game -> game that updates the state of the game
state game -> state returns wether a game is incomplete, won by player1 or won by... |
Reachability is defined as follows:
a digraph $G = (V, E)$ and two vertices $v,w \in V$. Is there a directed path from $v$ to $w$ in $G$?
Is it possible to write a polynomial time algorithm for it?
I asked this question on mathematics and got no answer by far.
|
Find the weight of the lightest path from u to v the goes through node a or/and b.
Do you have a suggestion on how it can be done?
|
Can a Boolean circuit by itself be considered an algorithm (a single step algorithm if you like)? For instance say you have a simple tree circuit with two AND gates as the input gates feeding a single OR gate for a depth two circuit. Now change the AND gates to XOR gates, is it correct to say that I now have a differen... |
Hello for a homework I have to show that deciding whether a regex over $\Sigma = \{0,1\}$ descibes $\Sigma^*$ is $\mathsf{coNP}$ complete (this is irrelevant for the question though).
The thing which irrs me is that I think this problem is in $\mathsf{P}$.
Here is my argumentation:
Let $R$ be a regex, then we have $$L(... |
let $L_c$ be the class of all languages that have a polynomial reduction to some language L, for example if $L=SAT$ then $SAT_c=NP$.
Assuming know that $NP\neq P$ we know that there exist languages that are not NP-hard and not in P, i.e. those in NPI. My question is there a language L in NPI such that $L_c \setminus \{... |
In database theory, there is a notion of transitive closure over relations. I am wondering if join operator over relations is also a special case of transitive closure?
|
I am trying to solve problem of preventing oversell of limited resources.
Consider resources (people) who are described by set of properties where each property belongs to different category (example properties from four categories: male, age 25-30, 2 children, interested in games).
Buyers want to allocate access to r... |
First I apologize if the title is unclear, but I didn't find anything better.
I'm solving a differential equation that has two parameters , here denoted by points of a plane.These parameters are real numbers. For some points of the plane (or, equivalently, for some parameters of the differential equation) , the solutio... |
I would like to build an online web-based machine learning system, where users can continuously add classified samples, and have the model updated online. I would like to use a perceptron or a similar online-learning algorithm.
But, users may make mistakes and insert irrelevant examples. In that case, I would like to ... |
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