Problem Detail: The max k-cut problem is: Given an undirected graph G= (V;E) with nonnegative edge costs, and an integer k, find a partition of V into sets $S_1,cdots,S_k$ so that the total cost of edges running between these sets is Read More …
Author: ignougroup
[Solved]: If $f(n) = Theta(g(n))$, do both functions bound each other for all $n$ or only sufficiently large $n$?
Problem Detail: The following is an excerpt from CLRS: $Theta(g(n))= { f(n) mid text{ $exists c_1,c_2,n_0>0$ such that $0 le c_1 g(n) le f(n) le c_2g(n)$ for all $n ge n_0$}}$. Assuming $n in mathbb{N}$, I was unable to find $f(n)$ Read More …
[Solved]: Complements of Linear Bounded Automata?
Problem Detail: Would switching the accept and reject states of an LBA A create a new LBA we’ll say A’ in which the language of A’ is the complement of the language of A? I believe the answer is yes just Read More …
[Solved]: Time complexity of proximity search in distance matrix
Problem Detail: I am a high school student computationally studying the 3-dimensional structure of chromosomes by 40 kilobase loci. In a nutshell, loci that are close in space tend to express their genes at the same time ― loci are different Read More …
[Solved]: How do locks work?
Problem Detail: Suppose I have an application with two threads, which both use the same resource. Normally, a synchronized block keeps these threads from messing with the resource in a way the user doesn’t expect. I understand why you do this, Read More …
[Solved]: What are appropriate isomorphisms between formal languages?
Problem Detail: A formal language $L$ over an alphabet $Sigma$ is a subset of $Sigma^*$, that is, a set of words over that alphabet. Two formal languages $L$ and $L’$ are equal, if the corresponding sets are extensionally equal as subsets Read More …
[Solved]: Direct NP-Complete proofs
Problem Detail: I’m just starting to learn about NP-completeness. While I understand that reducibility plays a key role in this, I’m astonished how few problems I’ve been able to find who’s proof that they are NP-Complete is not based on reduction Read More …
[Solved]: Algorithm to shrink a DFA by introducing nondeterminism?
Problem Detail: This is somewhat related to another question I asked, but I feel it’s different enough to warrant its own question. I’m doing research where I’m trying to find the structure of complements of a certain class of finite languages. Read More …
[Solved]: Number of Independent Sets in a tree
Problem Detail: (I’ve been stuck on this homework assignment for far too long) I need to find the number of independent sets in a tree. For example, say the set of nodes in a tree is {A, B, C, D, E}. Read More …
[Solved]: Showing that the entropy of i.i.d. random variables is the sum of entropies
Problem Detail: The shannon entropy of a random variable $Y$ (with possible outcomes $Sigma={sigma_{1},…,sigma_{k}}$) is given by $H(Y)=-sumlimits_{i=1}^{k}P(Y=sigma_{i});log(P(Y=sigma_{i}))$. For a second random variable $X=X_{1}X_{2}…X_{n}$, where all $X_{i}$’s are independent and equally distributed (each $X_{i}$ is a copy of the same random Read More …
