Problem Detail: If you have a forest implementation of disjoint sets, and have the union by weight/rank heuristic where you append the smaller one. Then why is the worst case running time Θ(m log n)? (m is the number of disjoint Read More …
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[Solved]: Is there a computationally reasonable algorithm for generating a set of polygons from a set of 2d points?
Problem Detail: Is there a known/existing algorithm for taking a 2D canvas covered in arbitrarily/randomly distributed points and dividing it entirely into a set of non-overlapping polygons? An example of the kind of result I’m looking for: Asked By : CaptainRad Answered Read More …
[Solved]: Why are weights of Neural Networks initialized with random numbers?
Problem Detail: Why are neural networks initial weights initialized as random numbers? I had read somewhere that this is done to “break the symmetry” and this makes the neural network learn faster. How does breaking the symmetry make it learn faster? Read More …
[Solved]: Importance of recursion in computability theory
Problem Detail: It is said that computability theory is also called recursion theory. Why is it called like that? Why recursion has this much importance? Asked By : user5507 Answered By : Andrej Bauer In the 1920’s and 1930’s people were trying to Read More …
[Solved]: complexity of decision problems vs computing functions
Problem Detail: This is an area that admittedly I’ve always found subtle about CS and occasionally trips me up, and clearly others. recently on tcs.se a user asked an apparently innocuous question about N-Queens being NP hard, But it got downvoted Read More …
[Solved]: How to show composition of one way function is not such?
Problem Detail: I was wondering how should I proceed in order to show that the composition of (say) two one-way functions (either weak or strong or both together) is not a one-way function? Specifically: Say $f$ and $g$ are one-way functions Read More …
[Solved]: Algorithm Request: “Shortest non-existing substring over given alphabet”
Problem Detail: I’m looking for an (efficient) algorithm to solve the following problem: Given a string $S$ and a set of characters $M$, find the shortest string composed only of characters in $M$ that is not contained in $S$. Try as Read More …
[Solved]: Is it compulsory that every infinite set be non regular?
Problem Detail: I am confused regarding the statements provided by one of our faculty regarding “Is it compulsory that every infinite set is non regular though every finite set is a regular set”. Providing this example: $$L= { 0^n 1^n | Read More …
[Solved]: Is Karp Reduction identical to Levin Reduction
Problem Detail: Definition: Karp Reduction A language $A$ is Karp reducible to a language $B$ if there is a polynomial-time computable function $f:{0,1}^*rightarrow{0,1}^*$ such that for every $x$, $xin A$ if and only if $f(x)in B$. Definition: Levin Reduction A Read More …
[Solved]: Does an abstract syntax tree have to be a tree?
Problem Detail: Does the output of a parser have to be a tree or could it also be general graph? Moreover, is there any existing language or a plausible one that uses general graphs representation instead of trees for their syntax? Read More …
