Problem Detail: The pumping lemma for regular languages can be used to prove that certain languages are not regular, and the pumping lemma for context-free languages (along with Ogden’s lemma) can be used to prove that certain languages are not context-free. Read More …
Author: ignougroup
Reducing directed hamiltonian cycle to graph coloring
Problem Detail: The 3-SAT problem can be reduced to both the graph coloring and the directed hamiltonian cycle problem, but is there any chain of reductions which reduce directed hamiltonian cycle to graph coloring in polynomial time? Asked By : Johan Sannemo Read More …
Show that Vertex-Cover is NP-complete, using Stable-Set
Problem Detail: My task is to give proof, the Vertex-Cover problem is NP-complete, assuming it’s already shown that the Stable-Set problem is NP-complete, too. My approach: i know, Stable-Set is NP-complete, and all Problems that are NP-complete can be reduced to Read More …
How to use a greedy algorithm to find the non-decreasing sequence closest to the given one?
Problem Detail: You are given n integers $a_1, ldots, a_n$ all between $0$ and $l$. Under each integer $a_i$ you should write an integer $b_i$ between $0$ and $l$ with the requirement that the $b_i$’s form a non-decreasing sequence. Define the Read More …
What problem does cache coloring solve?
Problem Detail: According to what I have read from two different sources, cache coloring is (was?) required in order to: Counter the problem of aliasing: Prevent two different virtual addresses with the same physical address from mapping to different cache sets. Read More …
Star free language vs. regular language
Problem Detail: I was wondering, since $a^*$ is itself a star-free language, is there a regular language that is not a star-free language? Could you give an example? (from wikipdia) Lawson defines star-free languages as: A regular language is said to Read More …
Upper Bound on Runtime of Memoized DP Algorithms
Problem Detail: I find it fairly easy to generate an upper bound for nearly any iterative solution (e.g. look at the limits on each loop, etc.), and can oftentimes create an upper bound for normal recursive functions. However, I am now Read More …
B-Tree and how it is used in practice
Problem Detail: I understand what a B-Tree is (I already implemented a B-Tree in Java with insert and delete methods that preserve the invariant). However I do not understand exactly how it is used for example for file systems or databases. Read More …
What are the mathematical prerequisites for adaptive machine learning algorithms?
Problem Detail: I am a PhD student in Computer Science who switched his PhD a little bit towards ML algorithms combined with something else… I am an expert in that something else, say image processing, but not an expert in Machine Read More …
What would we call this datastructure?
Problem Detail: Suppose we have a datastructure that is a list containing elements that are either a leaf or another layer of the datastructure (recursively defined). What would we call this? It isn’t a tree, since it has variable number of Read More …