Problem Detail: I’m trying to understand the approach to constructing a PDA which accepts the language { $a^i b^j c^k mid i,j,k geq0, i+2k = j$ } Asked By : Iancovici Answered By : Patrick87 Your language is equivalent to the language $a^ib^ib^{2k}c^k$, Read More …
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Differences between Fuzzy C-Means and EM
Problem Detail: When clustering a set of data points, what exactly are the differences between Fuzzy C-Means (aka Soft K-Means) and Expectation Maximization? In slide 30 and 32 of this lecture I found, it says that Soft K-Means is a special Read More …
Is the 0-1 Knapsack problem where value equals weight NP-complete?
Problem Detail: I have a problem which I suspect is NP-complete. It is easy to prove that it is NP. My current train of thought revolves around using a reduction from knapsack but it would result in instances of 0-1-Knapsack with Read More …
Kleene star and Kleene plus
Problem Detail: Let $Sigma$ be an alphabet. Have a look at following definitions frequently used in literature containing Kleene star and Kleene plus. $Sigma^* := Sigma^+ cup {varepsilon}$ $Sigma^+ := Sigma^* setminus {varepsilon}$ These definitions lead to different sets iff $varepsilon Read More …
Control flow graphs – Tree decomposition
Problem Detail: Considering above terminologies for drawing control flow graphs for any program, it is very simple. For example : While A if B do .. else do .. end while For above example, while doing decomposition, I can say Read More …
Can a regular expression be infinite?
Problem Detail: I know that languages which can be defined using regular expressions and those recognisable by DFA/NFA ( finite automata ) are equivalent. Also no DFA exists for the language ${0^n1^n|n ge 0}$. But still it can be written using Read More …
Performance of row- vs. column-wise matrix traversal
Problem Detail: Scott Meyers describes here that traversing a symmetric matrix row-wise performes significantly better over traversing it column-wise – which is also significantly counter-intuitive. The reasoning is connected with how the CPU-caches are utilized. But I do not really understand Read More …
Recurrences and Generating Functions in Algorithms
Problem Detail: Combinatorics plays an important role in computer science. We frequently utilize combinatorial methods in both analysis as well as design in algorithms. For example one method for finding a $k$-vertex cover set in a graph might just inspect all Read More …
Evolving artificial neural networks for solving NP problems
Problem Detail: I’ve recently read a really interesting blog entry from Google Research Blog talking about neural network. Basically they use this neural networks for solving various problems like image recognition. They use genetic algorithms to “evolve” the weights of the Read More …
Is there any theoretically proven optimal compression algorithm?
Problem Detail: Is Huffman coding always optimal since it uses Shanon’s ideas? What about text, image, video, … compression? Is this subject still active in the field? What classical or modern references should I read? Asked By : Zeta.Investigator Answered By : Arani Read More …
