Problem Detail: Suppose I give you an undirected graph with weighted edges, and tell you that each node corresponds to a point in 3d space. Whenever there’s an edge between two nodes, the weight of the edge is the distance between Read More …
Category: Uncategorized
[Solved]: Complete Problems for $DSPACE(log(n)^k)$
Problem Detail: We know that the $polyL$-hierarchy doesn’t have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy? To be precise: Does the class $DSPACE(log(n)^k)$ have complete problems Read More …
[Solved]: A “triangular” data structure for commutative relationships
Problem Detail: 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 Read More …
[Solved]: Is path induction constructive?
Problem Detail: I’m reading through the HoTT book and I have a hard time with path induction. When I look at the type in the section 1.12.1: $$text{ind}_{=_A}:prod_{C:prodlimits_{x,y:A}(x=_Ay)to mathcal{U}} left( left(prod_{x:A}C(x,x,text{refl}_x)right) to prod_{x,y:A}prod_{p:x=_Ay} C(x,y,p) right),$$ I have no issue understanding what Read More …
[Solved]: What is a dichotomy? Whether 2-SAT itself is a dichotomy of SAT?
Problem Detail: Recently, I am reading papers about dichotomy. I do not understant what condition can be called as a dichotomy? What is the meaning of “a question is either in P or in NP–complete“? (assume P $neq$ NP) For example, Read More …
[Solved]: Is $log(n!)$ in $Theta(n log(n))$?
Problem Detail: I had two questions on my automated test which I don’t understand the answer for. $log(n!) = log(ncdot (n-1)cdot cdots cdot 2cdot 1) = log(n)+log(n-1)+….+log(1)$. So it is in $O(nlog(n))$. But is it also in $Omega(n log(n))$? I don’t Read More …
[Solved]: Universal/existential quantification?
Problem Detail: I’m struggling to understand the purpose of universal and existential quantification of types. I’m playing around with writing a toy language based on the calculus of constructions. I’ve been reading about Morte and Henk to help me get a Read More …
[Solved]: Understanding Closest Pair Algorithm (CLRS)
Problem Detail: I’m reading CLRS Section 33.4 Finding the closest pair of points. At exercise 33.4-2 they say 33.4-2 Show that it actually suffices to check only the points in the 5 array positions following each point in the array Y’ Read More …
[Solved]: High Dimensional Data Structures
Problem Detail: I have a 20-dimensional dataset, with a large amount of data points. I would like to have each dimension discretized into bins. Per bin, I would like to be able to access two neighbours per dimension (i.e. +1 and Read More …
[Solved]: What mechanisms prevent a process from taking over the processor forever?
Problem Detail: Suppose a process keeps running code (e.g. an infinite loop). How can other programs take over? What prevents the process from remaining active forever? Asked By : Dionysus Answered By : Gilles Various peripherals are connected to the main processor. When Read More …
