instruction stringlengths 35 29.1k |
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I have an NLP problem and a potential solution, but I’m a bit green here, so I’m looking for some validation or alternative suggestions.
Background
I have two types of documents: one is a set of short statements of an organization's goals and objectives (“Goals”, from here on. ~500 docs, ~100 words/doc. New documents m... |
I have been trying to understand, what is the actual meaning of 2 graphs being:
Symmetric
Transitive
Reflexive
A graph being a subgraph of another graph
And other similar relations if let's say I have two graphs containing 1000's of nodes and edges. Then, what do these terms mean w.r.t to those 2 graphs?
|
As input I have two sets of points in RN, typically for large N, for example N=40. Supose both sets have m elements:
S = s1 ... sm
T = t1 ... tm
Semantically both sets are equal, but due to noise (of whatever kind) on the R^N points, elements which should be semantically the same still have a distance larger than 0.
Wh... |
I have a question that, no matter how much I think about, I do not have the answer to. The question is what exactly is computer science? The reason I am asking is that I went into college thinking computer science was going to be about software engineering disciplines and deep study in the realm of application and pr... |
Here is an attached link to a problem, the Substring query problem
that I am trying to solve. It requires the use of suffix automaton,but I could not understand what is a suffix automaton. Can anybody explain.
|
In Sipser, there is a proof I don't understand.
First he established the undecidability of $A_\mathrm{TM}$, the problem of determining
whether a Turing machine accepts a given input.
$$A_\mathrm{TM}=\left\{\left \langle M,w \right \rangle\mid M \text{ is a TM and }M \text{ accepts }w\right\}\,.$$
Then defined $\mathr... |
I'd like to create a modified mergesort algorithm to return the k smallest elements of an array. The mergesort algorithm below sorts an unordered array of size n. How do I modify the algorithm so that it returns the k smallest elements of the array?
A = [1...n]
Mergesort (A,p,r) //start with p = 1 and r = A.length
... |
Given a string $S$ of length $n$ characters, is it possible to calculate the hash of its substring $[i, j]$ (from index $i$ to $j$, both inclusive) in $O(1)$ using some form of precomputation? Can we use a modification of the rolling hash?
The following is a similar problem to my question. In it the string was given in... |
Given a set $X$ of $n$ points in the real plane, designated by their Cartesian coordinates, find the extreme spread of the points, which is defined by
$\qquad\displaystyle \mathrm{ES} = \max_{1 \leq i,j \leq n}: \sqrt{(x_i - x_j)^2 - (y_i - y_j)^2}$,
i.e. the largest Euclidian distance between any two points in the set... |
Is there any polynomial procedure to decide if 2 deterministic finite automatas decide the same language?
|
I am attempting to write a Finite State Transducer module in OCaml, because I think it's a good exercise, which is because I have been teaching myself Natural Language Processing.
You typically construct finite automata using regular expressions, for example (a | b).
What language does one typically use to construct Fi... |
I am looking for references (pedagogic and beginner friendly!) to these two topics,
hierarchical temporal memory algorithms applied to deep planning problems
(multi-layer) neural networks trained via SGD (after some bottom-up pre-learning using autoassociator / RBM algorithms)
Can someone help with a reference (hope... |
Could please tell me the language generated by this grammar?
S->iS |iSeS|ε
|
My professor presented a method to find shortest paths using the min-sum multiplication and Boltzmann distribution.
He multiplies the adjacency matrix many times and takes the $\beta$ of Boltzmann very large to find it.
I cannot understand at all the method from my notes, and I cannot find it in my book (Papadimitriou)... |
I am looking for the opinions of more experienced programmers as to the effectiveness of writing programs in Block Programming Environments such as Scratch or App Inventor as opposed to High Level Languages such as C++, Python or Java.
I have already done some research and here are some examples of links that have been... |
I read that a supercalar processor has redundant functional units. One can read this e.g. on Wikipedia.
How do such redundant units work?
Is a complex instruction (for accelerating heavy process, for example Instructions used in Intel IPP, Integrated Performance Primitives) decomposed in micro operations befaure being... |
I was looking for comments about SMT and got several responses. The last one looks strange:
Simultaneous multithreading, which can only be implemented on a multicore system, executes the different threads on different cores, or on different processing units on the same core ("superscalarity").
Why can SMT be impleme... |
I was looking for a way to easily store and access a symbol table using the least memory and code as possible and I went with a BST. Symbols, however, tend to be defined in order as in foo0, foo1, foo2... so tree balance is an issue.
I considered balancing and auto-balancing algorithms, but then I realized that the has... |
First of all, excuse me if I write a lot, I tried to summarize my research so that everyone can understand.
R. Baeza-Yates and M. Regnier published in 1993 a new algorithm for searching a two dimensional mm pattern in a two dimensional nn text. The publication [1] is very well written and quite understandable for a nov... |
It's well known that linear congruential generators have a full period only if a few properties are fulfilled.
Now I need a LCG that does not generate a full period in 2^32 (easy to find, just violate one requirement) and I need one of those values in the period that's not used.
Is there any clever math trick/algorithm... |
I'm studying CPU's and I know how it reads a program from the memory and execute its instructions. I also understand that an OS separates programs in processes, and then alternate between each one so fast that you think that they're running at the same time, but in fact each program runs alone in the CPU. But, if the O... |
I am using Sedgewick's Algorithms (4th ed) to learn Knuth-Morris-Pratt substring search algorithm. The key step is construct the DFA array corresponding to a given pattern. The authors say:
The key observation is that the characters in the text that would need to be rescanned are precisely pat.charAt(1) through pat.ch... |
I'm trying to check how general and valid protocol suite system ( layered structure ) are.
Does anyone know if radio communication ( broadcast ) via AM or FM , for instance can be viewed in the light of a layered structure ( for example, the OSI model ) as operating at least in one or more in layers ? Maybe could it be... |
I am a 2nd year computer science student. We all have subjects about Data Structures, Theories, more more theories we all know that i have a subject this semester Design Analysis of Algorithms.
So my question is. How do you guys understand well all the Algorithms? Any technique?
To snap out the confusion about my que... |
My Masters thesis is on task graph scheduling for multi core processors. I have developed a new task clustering and scheduling algorithm. I wanted to know about how can I find data to compare it with my work? Me and my supervisor have tried contacting the authors of a few similar works for data but none of them is shar... |
I'm looking into PCFG sentence grammar dependency structure parsing using StanfordNLP PCFG parser. It generates tree structures represented as a string like this:
Happy new year => (ROOT (VP (VBN Happy) (NP (JJ new) (NN year))))
Or in a more visual way, the tree structure looks like this:
(ROOT
(VBN (JJ Happy)
... |
A multiplication table is symmetric over a diagonal, so only about $n^2/2$ of the elements in an $n \times n$ multiplication table contain unique information. Same goes for addition tables. In fact, the same is true for any table that represents a commutative relationship. Is there a data structure that can take advant... |
When developing algorithms in quantum computing, I've noticed that there are two primary models in which this is done. Some algorithms - such as for the Hamiltonian NAND tree problem (Farhi, Goldstone, Guttman) - work by designing a Hamiltonian and some initial state, and then letting the system evolve according to the... |
Suppose I have a set $A$ of elements in $\{1, \ldots, n\}$, given as an unordered list.
I would like to compute the complement of $A$, i.e., I would like to produce an unordered list of entries in $\{1, \ldots, n\}$ but not in $A$.
One way to do this is to sort the entries of $A$ and then go through them and list all... |
I'm studying a major in CS. I'm interested in taking a few extra courses, specifically math to improve my knowledge as future computer scientist.
Right now I'm thinking to take Matrix Fundamentals but I'm not sure if it is going to help me in my CS career. What are its uses apart from arrays in programming?
|
This a problem in a computer architecture course that's giving me some trouble:
You have an application whose memory access pattern is a stream and its entire data set is 128kB. The data cache in your machine has a capacity of 64kB. It is word-addressable and direct-mapped with 32B lines. It is able to fetch one line ... |
Please give me an example of an unsatisfiable quantified 2 CNF formula. I need it in my proof and I am unable to think of one.
I am looking for such an unsatisfiable
quantified 2 CNF formula which gets satisfiable if the ordering of prefix is changed.
|
Given $a_1, a_2, a_3, \dots,a_7$ where $a_i \in \{0,1\}$. How to calculate sum of all binary number of the form
$$\over {1a_1a_2*a_3**a_4***a_5a_6a_7}$$
where $*$ represent the position of running digits.
I am thinking about a dynamic programming solution.
|
This is a graph theory and partial ordering problem. Consider a set of triples {(di,ai,ci)}i=1...N, which specify edges between two nodes A and B, d denotes a departure time, a an arrival time and c a cost. Technically there can be multiple incomparable costs, for example in $ and % chance that your goods arrive safely... |
I am trying to do optimization of a voice activity detection function, which is a function with continuous parameters. This is easily accomplished with genetic algorithms, simulated annealing, and tabu search, but I'm somewhat confused on how to accomplish this with Ant Colony Optimization (ACO).
From what I've read, ... |
Problem (tl;dr)
Given a context free grammar, $G$, find a set of strings that take $G$ through every production it has at least once.
How and how fast can it be done?
Background
I'm working on a compiler whose parser is implemented with a tool similar to Yacc+Antlr. I've written up most of the parser code, and I'd lik... |
in TAOCP vol3 2nd Edtion's 5.4.1R Replacement Selection, there is a paragraph describing a data structure and example for Replacement Selection as follows:
the algorithm below uses a data structure containing $P$ nodes to represent the selection tree; the $jth$ node $X[j]$ is assumed to contain $c$ words beginning in $... |
I'm looking around for a good garbage collection technique for my language and found this paper, where Benjamin Goldberg describes a garbage collection technique for strongly typed languages, which removes the need for type information during runtime.
Briefly, this is done by placing a pointer to a garbage collection f... |
I am to prove that monotone boolean formula satisfiability checking when at most k variables are set to 1 is an NP-Complete problem. Proving that it is in NP is easy, but I'm having difficulty showing that it is in NP-Hard. I have seen this, but I would rather not use its solution, as the textbook for the course I am... |
I am currently trying to get some intuition on the concept of First Order reductions, and have come across this exercise question by Immerman, dubbed "Everything is a Graph".
Given some arbitrary relational structure $S$ of some vocabulary $\sigma$, show that there are first-order queries $I$ and $I^{-1}$, such that $G... |
I'm not sure this is on-topic or even the right website, please point me in the right direction if not.
I was wondering why computers are so incredibly complex. This question is as naive as it sounds, I'm really just looking for a nice explanation of why computers can't be like the airplane from Blyton's The Faraway Tr... |
Let $G$ be a directed graph, with a single source node $s$. I want to find a collection of paths that cover every edge of $G$ (i.e., every edge of $G$ appears in at least one of these paths), where each path must start at $s$. The cost of a collection of paths is the sum of the lengths of the paths.
Is there an effic... |
If I have a program, its instructions are stored on the hard drive. When I double-click the executable the pages of memory for this process must get loaded in to RAM. However, for the pages to get loaded in to RAM, the CPU must already have resolved the virtual address to physical address. The latter requires the TLB t... |
I am not a formally trained guy on Complexity theory, but due to interest I am learning it. Based on different feedbacks, I have started my journey with Micheal Sipser's "Theory of Computation" (2013 edition). My question is based upon some statements from the book. My sincere apologies if the question is meaningless.
... |
I know that Hamiltonian cycle problem is $NP$-complete for 2-connected planar bipartite cubic graphs.
I'm interested in non-trivial infinite subclass of cubic graphs where the Hamiltonian cycle (path) problem is efficiently solvable. I tried the graph class database but could not find any such class graph.
Is there an... |
As far as I understand it, when you delete a file from trash/recycle bin the file isn't actually erased from memory but is instead marked as being okay to be over written.
So, my question is as to why this is the case. Is it simply for speed/convenience reasons or is actually deleting data just a much harder (or imposs... |
I was given this question by a friend:
"You are given 3 sets of size n, X,Y and Z. Devise an algorithm to find maximum number of different pairings (u,v,w,x) such that u,v,w,x belong to X,Y,Z and X respectively (u is not equal to x) and gcd(u,v,w,x)>1."
My approach is to create new sets S and T, such that S contains pa... |
How can I assess and derive the time complexity of the BBP formula?
$$
BBP(n)=4S(1,n) - 2S(4,n) - S(5,n) - S(6,n)
$$
where
$$
S(j,n) = \sum_{k=0}^n{\frac{16^{n-k}mod(8k+j)}{8k+j}}+\sum_{k=n+1}^{\infty}{\frac{16^{n-k}}{8k+j}}
$$
Note that the modulo is evaluated using the binary modular exponentiation algorithm (which i... |
I have a $n \times m$ matrix $M$ and a permutation of sequence $P$ of numbers from $1$ to $n$.
I have to fill the matrix using numbers $1$ to $n \times m$ in such a way that for each row $i$, the function $f(i) > 0.5$ where:
$f(i)$ is the probability that a number chosen randomly from row $i$ will be greater than a num... |
AES NI seems to perform AES operations much faster than doing in software. However, if I have a machine with a large number of cores (say 32 cores), can I perform 32 AES encryptions using AES NI instruction i.e. one per core? Or can I just run one AES instruction?
|
I have a really nasty problem (for me) at hand and I was wishing some of you may know an efficient algorithm to solve it. Thanks to all of you in advance.
My problem
I have a set of elements (that I would describe as a graph) that may be of three categories:
Provider nodes
Consumer nodes
Interconnections between node... |
I'm looking for an algorithm for doing iterated find/replace, where the act of finding the replacement list of tokens for a given find is slow.
Specifically: I have a function, f, that maps a sequence of tokens to either a shorter list of tokens or None. However, it is slow.
I want to repeatedly try to replace the (fir... |
Given a connected graph $G$ and a vertex $v$, is it polynomially solvable to find a maximal cardinality set of edges incident to $v$, which deletion (still) leaves vertex $v$ to be connected with all the other vertices in $G$?
|
The wikipedia page on multiplication algorithms mentions an interesting one by Donald Knuth. Basically, it involves combining fourier-transform multiplication with a precomputed table of logarithmically-sized multiplications. It runs in linear time.
The article acts like this algorithm somehow doesn't count as a "true"... |
I know from Sedgewick's book on algorithms that the max depth of any node x from a set of N nodes is at most log2(N) applying the algorithm(which says to put the shorter tree beneath to avoid tall trees) and he gives an understandable proof by induction. The thing is that I have trouble visualising that result apart fo... |
I'm having difficulties with analyzing the worst-case runtime of this following case:
I'm given an array that has $n$ natural numbers. Out of all $\binom{n}{2} = \frac{n(n-1)}{2}$ possible pairs there are $\frac{n(n-1)}{2} - 5n$ inversions. Inversion is defined like this: $a[i] < a[j],\ i>j$.
So of course you can sort... |
Im working on a modified A Star algorithm, that instead of attempting to find the shortest path, it tries to find the longest past, or in my specific case, the highest weighted path.
I have some number of classes, each with a list of unique nodes, with each node having its own value. Im attempting to determine the bes... |
Wikipedia states on sparse languages that
There is a Turing reduction (as opposed to the Karp reduction from Mahaney's theorem) from a NP-complete language to a sparse language iff NP $\subseteq$ P/poly.
Is that correct in that it is so far proven for an arbitrary Turing reduction and not a limited P-time reduction... |
Problem: Given a collection $S$ containing $|S|=n$ rectangles defined by dimensions $(x,y)\in R^2$ (width and height of rectangles are real numbers), find the rectangles with the minimum area ($A_i = x_i * y_i$) where $(x_i \geq a)$ and $(y_i \geq b$) for any $(a,b) \in R^2$.
The naive solution $F(S,a,b)$ will solve th... |
The Schönhage–Strassen multiplication algorithm works by turning multiplications of size $N$ into many multiplications of size $lg(N)$ with a number-theoretic transform, and recursing. At least I think that's what it does because there's some other cleverness and I really don't understand it well enough to summarize ac... |
[This regarding to Computational geometry in CS]
Let's say that I have a graph G which contains v vectices and e edges, For instance a veronoi diagram VD(G).
I'd like to build a trapezodial map out of my given graph,
Is that possible to build trapezodial map in linear time for a given graph, Instead of O(nlogn) regula... |
I am searching for substrings that satisfy a given first order formula in a moderately sized text. The formula is made out of usual $\wedge, \neg, \exists$ and predicates Equals(x, "some string"), Before(x, y) and similar, where variables are pairs indices denoting substrings.
If the text is $n$ symbols long and the fo... |
Current floating point (ANSI C float, double) allow to represent an approximation of a real number.
Is there any way to represent real numbers without errors?
Here's an idea I had, which is anything but perfect.
For example, 1/3 is 0.33333333...(base 10) or o.01010101...(base 2), but also 0.1(base 3)
Is it a good idea ... |
An i18n-style abbreviation is one in which multiple letters are shortened to that number of letters. E.g., "internationalization" -> "i18n" ("nternationalizatio" is substituted with its length 18). Other abbreviations include "in17n", "i17on", "in16on", etc. I see a pattern in which words with at least 3 characters hav... |
Consider a variation of the set cover problem in which the size of the subsets is no larger than a constant $k$. Is this variation still NP-hard?
|
Assume that we have 10 points. If all those points are on the same plane, they all are coplanar. But some of them might be at a different place. That disrupts the structure of the plane if we were to draw the surface that passes from all the points.
I need a metric that tells me how fine the structure of the plane is p... |
I am trying to understand what BNF, metalanguage, and metasyntax are.
From https://proofwiki.org/wiki/Definition:Metalanguage
A metalanguage of a formal language is a formal language used to
specify the formal language (make statements about the formal
language).
The object language of a metalanguage is the langua... |
If you had a polynomial time algorithm for determining boolean satisfiability how would you prove/disprove a conjecture like the Reimann-Zeta hypothesis (or the Pythagorean theorem for that matter) from axioms?
|
For a formal language $L \subseteq \Sigma^*$ over an alphabet
$\Sigma$. From https://proofwiki.org/wiki/Definition:Syntax
The syntax of a formal language is its structure, and is specified by
a formal grammar of the formal language.
From http://en.wikipedia.org/wiki/Syntax_%28logic%29
In logic, syntax is anything... |
According to page 53 of Modern Computer Arithmetic (pdf), all of the steps in the Schönhage–Strassen Algorithm cost $O(N \cdot \lg(N))$ except for the recursion step which ends up costing $O(N\cdot \lg(N) \cdot \lg(\lg(N)))$.
I don't understand why the same inductive argument used to show the cost of the recursive step... |
The paper On The Power of Multi-prover Interactive Protocols by Fortnow, Rompel, Sipser states the following:
There are provers $P_1, P_2, \dots, P_k$ in a multi-prover interactive proof system such that $k$ is polynomial in the size of the input. The value of $k$ cannot exceed a polynomial because this would prevent ... |
Preamble
I can't understand what are the advantages and disadvantages of microcoded processor architecture and hardcoded one.
Basically what I understood is that a microcode architecture divides an istruction in more microinstructions. I didn't found much documentation written in a simple way (too much complicated) so ... |
I am building a strategy game where multiple units(5 - 20) is fighting each other in the same time.
I have a logic part that calculate those actions for each turn, and than pass it to the game engine to animate. This is the list of action that I currently supporting:
perform attack
perform miss
perform taking damage
... |
In Schönig and Pruim's Gems of Theoretical Computer Science, the following statement is made:
'Post's Problem', as it has come to be known, is the question of whether there exist undecidable, computably enumerable sets that are not Turing equivalent to the halting problem. In particular the answer is yes if there are ... |
Let $G=(V,E)$ be a DAG. A subset $A \subseteq V$ is called a kernel if for all $u,v \in A$ $uv \notin E$ and for all $v \in V-A$ there exists an $a \in A$ such that $av \in E$ (note again, this is a directed graph).
I need to find an algorithm that runs in $O(V+E)$ that upon giving a DAG $G$, would find a kernel in the... |
As a hobby, I am writing a simple and primitive distributed web search engine. It occurred to me that it currently has no protection against malicious peers trying to skew the search results.
The principle idea of the project is:
To store the inverse indices and ranking factors in a Kad (Kademlia) DHT (Distributed H... |
Under the hypothesis that P=NP, many cryptographic protocols are no longer secure (i.e. attacks are feasible).
The BB84 algorithm is based on the idea that by observing a quantum state, one has to (in quantum theory) disturb that state. This makes them efficient against eavesdropping.
Are quantum algorithms based on BB... |
Herbrand's theorem shows that any formula of first-order logic can be expressed as a disjunction of quantifier-free formulas of first-order logic.
Is this equivalent to saying that Herbrand's theorem shows that any first-order logic formula can be expressed in Conjunctive Normal Form (CNF)?
|
Normal human math notation treats juxtaposition as implied multiplication, e.g., $2x$ means $2$ multiplied by $x$. This does not seem to be a common feature of computer languages, although it was, for example, supposed to be included in the language Fortress (now a dead project).
Lexing and parsing such a language seem... |
I am building a strategy game where units can interact with each other.
As input I am getting a list of actions. I need to output a scheduler, that will tell when to start each action. The goal is to find the shortest time combination of all the actions.
Action is defined as interaction between two users or user with h... |
I hope the Computer Science section is the appropriate place to ask this question. I’m working on profiling some data sets and I am a bit tripped up on something, I was hoping I could get some assistance.
Part of my project is to determine whether some of my data is an integer and whether is a continuous or discrete q... |
I asked this over on math.stackexchange.com, then I found out about this forum.
Suppose you have an $(n\times n)$-chessboard, together with a constraining function $C : n \times n \to 2$ where $C(i,j) = 1$ iff you're allowed to place a rook in the $ij$-square. Consider the problem:
Can $n$ non-attacking rooks be plac... |
I will state the problem:
Suggest an algorithm that works in $O(|E| + |V|log|V|)$ time that checks if there are negative cycles in a graph.
So, I saw the runtime, and I immediately said we need to use Dijsktra's implementation with a fibonacci heap.
I suggested the following:
Run dijkstra, and mark the distances ar... |
What advantages and disadvantages does a CISC instruction set have relative to a RISC instruction set with respect to the ease of developing a functioning compiler and the ease of developing a highly optimizing compiler?
|
In the RAM model, you're allowed to do unbounded indirect access (pointers can be arbitrarily large and still fit in a single machine word).
In the Bit Complexity model (no wiki article, sorry), machine words are constant sized. So storing the address of an entry in a table of size $N$ would require $O(lg(N))$ words.
T... |
I created a program that simulates the fcfs scheduling algorithm. First I implemented it for a single core, then modified it for four homogenoues cpus.
I compared the results with several datasets, and for the most part they are identical.
I understand fcfs is nonpreemtive, so there are no context switches. Then each ... |
In particular POS tagging, dependency and constituent parsing. This is not really my field of study but I would really like to be able to make informed claims on what precisions current top systems achieve (and what top systems for each task are).
This paper of a (high quality) system (http://arxiv.org/abs/1103.0398) ... |
Does anyone know of a non-trivial reduction from XORSAT to 2-sat since they are both in P? (By non-trivial I mean one that does not just solve the instance of XORSAT and map it to a fixed instance of 2-sat. Rather I'm looking for a way to solve XORSAT by a different method other than just using Gaussian Elimination o... |
Wouldn't non-digital computers, those that use a base higher than 2, be faster and more efficient? Especially with Moore's law reaching its limit, wouldn't circuits that have three, four or five states have advantages? Are there computers like that?
|
What string operations are basic in the sense that the other string operations can be represented in terms of them? Here is a list of string operations off the top of my head (not necessarily a complete list, and your addition is welcome):
reversal of a string
concatenation of two strings
repetition of a string a fini... |
From Wikipedia:
A logical system or, for short, logic, is a formal system together with a form of semantics, usually in the form of model-theoretic interpretation, which assigns truth values to sentences of the formal language, that is, formulae that contain no free variables. A logic is sound if all sentences that ca... |
Wikipedia says that lambda calculus is a formal system. It defines lambda calculus by giving its alphabet, and inductively describing what is inside its formal language.
Since lambda calculus is a formal system, what are its
axioms and
inference rules?
Does lambda calculus have semantics? If yes, how does an inter... |
I have a problem, and I appreciate it if you could share your thoughts.
Assume that I have a graph. Assume that I have $k$ iterations. I want to find only one independent set (IS) in the graph in each iteration. Then, I will increase a counter for those vertices that are in the selected IS. Initially, the counter for ... |
Let $k\in \mathbb N$
I'm looking for a small NFA build for the language of concatenation of two words of the length $k$ which are index-wise different, i.e. $$L_k=\{u\cdot v \in \Sigma^* : |u|=|v|=k\wedge \forall i, u_i\neq v_i\}$$
Notice that since $k$ is fixed, $|L_k|=(|\Sigma|\cdot(|\Sigma|-1))^k$, and is regular as... |
I am solving a problem of information theory. The problem reads,
Consider a stationary memoryless channel specified by the channel matrix
$T = \begin{pmatrix}1-q&q\\r&1-r\end{pmatrix}$. Let the random variables $X$ and $Y$ be the input and the output of T, respectively. Let the input alphabet of $T$ be $\left\{0,1\... |
i<--2
while (i<n)
someWork (...)
i <-- power (i,2)
done
Given that someWork(...) is an O(n) algorithm, what is the worst case
time complexity?
I've found this question answered on this site with the solution of O(n log n), however I don't quite understand why. I know that the power function... |
I'm wondering if there are any $NP$-hard problems which are ``polynomial" in the average case. I think there are two ways to interpret this?
If $P \neq NP$, can there be an algorithm solving an $NP$-hard problem with amortized (average case) running time of $O(n^k)$ for a constant $k$?
Are there any problems which are... |
From http://www.seas.gwu.edu/~rhyspj/spring09cs145/lab8/lab82.html
The lambda operator does not bind every occurrence of its variable because "shadowing" can occur. A variable is bound by its nearest enclosing lambda.
In $(\lambda (x) ((y\,\, x) (\lambda (x) (x\,\, y))))$, the $x$ in $(y\,\, x)$ is bound by the outerm... |
I have a small user-item matrix (25k x 1.8k) describing how users liked or disliked some of the items. Users don't have any attributes but items have several features.
I would like to be able to predict, using this dataset, some of the hidden likes and dislikes.
I don't have experience in the field and am not particula... |
Most programming languages provide multi-way conditional constructs (like cond in Lisp, guards in Haskell, etc) that allow one to define program behavior according to different conditions. But most of them also implies a default top-down ordering: the next condition is checked only when all preceding conditions are un... |
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