Problem Detail: I’ve just read about R-Trees: The key idea of the data structure is to group nearby objects and represent them with their minimum bounding rectangle in the next higher level of the tree; the “R” in R-tree is for Read More …
Author: ignougroup
[Solved]: Can subtracting o(1) from the parameter of a function change its Θ-class?
Problem Detail: I would like to know if it is possible that two functions $f(n), g(n)$ can exist such that both of the following conditions are met: $g(n) = o(1)$ $f(n-g(n)) neq Theta (f(n))$ I though I found $1/n$ and $1/n^2$ Read More …
[Solved]: What do we know about NP ��� co-NP and its relation to NPI?
Problem Detail: A TA dropped by today to inquire some things about NP and co-NP. We arrived at a point where I was stumped, too: what does a Venn diagram of P, NPI, NP, and co-NP look like assuming P ≠ Read More …
[Solved]: Introduction into first order logic verification
Problem Detail: I am trying to teach myself different approaches to software verification. I have read some articles. As far as I learned, propositional logic with temporal generally uses model checking with SAT solvers (in ongoing – reactive systems), but what Read More …
[Solved]: Vapnik-Chervonenkis Dimension: why cannot four points on a line be shattered by rectangles?
Problem Detail: So I’m reading “Introduction to Machine Learning” 2nd edition, by Bishop, et. all. On page 27 they discuss the Vapnik-Chervonenkis Dimension which is, “The maximum number of points that can be shattered by H [the hypothesis class] is called Read More …
[Solved]: Proving that NPSPACE $subseteq$ EXPTIME
Problem Detail: I am following “Introduction to the theory of computation” by Sipser. My question is about relationship of different classes which is present in Chapter 8.2. The Class PSPACE. $P subseteq NP subseteq PSPACE = NPSPACE subseteq EXPTIME$ I am Read More …
[Solved]: Use closure properties to transform languages to $L := { a^nb^n : nin mathbb N }$
Problem Detail: For the purpose of proving that they are not regular, what closure properties can I use to transform the languages $L_a = { a^*cw mid w in {a,b }^* land |w|_a = |w|_b }$ and $L_b = {ab^{i_1}ab^{i_2}ldots ab^{i_n} Read More …
[Solved]: Proof of equivalence of parse-trees and derivations
Problem Detail: Intuitively, every derivation in a context-free grammar corresponds to a parse-tree and vise versa. Is this intuition correct? If so how can I formalize and prove such a thing? Asked By : saadtaame Answered By : saadtaame Theorem. Let $G = Read More …
[Solved]: Equality of NSpace and coNSpace classes
Problem Detail: I’m trying to decide which of the following statements are true: $mathsf{NSpace}(log log n) = mathsf{coNSpace}(log log n )$ $mathsf{NSpace}(lg^2n) = mathsf{coNSpace}(lg^2n)$ $mathsf{NSpace}(sqrt n) = mathsf{coNSpace}(sqrt n)$ I thought immediately that (1) is correct since $lg lg n < Read More …
[Solved]: lexicographic depth-first search complexity class
Problem Detail: It seems to me to be incorrect to say that lexicographic DFS is P-complete, since it isn’t a decision problem. There is a corresponding decision problem, first DFS ordering, which is known to be P-complete. However, I want to Read More …
