Problem Detail: I know that for every $k$-tape DTM that runs in time $O(t(n))$, there exists a 1-tape DTM that runs in $O(t^2(n))$, no matter how large the $k$ (the $k$-part is a formulation from Wikipedia). But what if $k=infty$? If Read More …
Category: Uncategorized
[Solved]: Are probabilistic search data structures useful?
Problem Detail: A SkipList provides the same $O(log n)$ bounds for search as a balanced tree with the advantage that rebalancing isn’t necessary. Since the SkipList is constructed using random coin flips, these bounds only hold as long as the structure Read More …
[Solved]: Complexity of a subset sum variant
Problem Detail: Is this variant of the subset sum problem easy/known? Given an integer $m$, and a set of positive integers $A = {x_1, x_2, …, x_n}$ such that every $x_i$ has at most $k=2$ bits set to $1$ ($x_i = Read More …
[Solved]: Showing that Independent set of size $k$ can be decided using logarithmic space
Problem Detail: An independent set $I$ is a subset of the nodes of a graph $G$ where: no 2 nodes in $I$ are adjacent in $G$. For natural number $k$, the problem $k-text{IND}$ asks if there is an independent set of Read More …
[Solved]: Construction of fair teams
Problem Detail: let’s say we have a set of players that we want to match into teams of aproximatly same strength, so that no team is much stronger than another team. Each team consists of two players. One player is taking Read More …
[Solved]: Select a subset of the columns in $2times n$ matrix, is it easy?
Problem Detail: I want to know if this problem is polynomial-time solvable or not? The problem is: Given a nonnegative integer-valued matrix of size $2times n$ and two nonnegative integer numbers $b<n$ and $c$. The question is: Find a subset of Read More …
[Solved]: User level threads are transparent to the kernel?
Problem Detail: Find whether given statement True or False? Explain. User level threads are transparent to the kernel? My attempt : False. Since, user level threads are managed by a user level library however, they still require a kernel system call Read More …
[Solved]: Why is NP not trivially equal to Co-NP? (a.k.a. what does Co-NP mean exactly?)
Problem Detail: I’ve been trying to wrap my head around Co-NP, and how it’s different to NP, but I am having some trouble. Co-NP is defined by Wikipedia as this: “A decision problem $mathcal{X}$ is a member of co-NP if and Read More …
[Solved]: Lambda Calculus Evaluation
Problem Detail: I know this is a simple question but can someone show me how $(lambda y. lambda x. lambda y.y) (lambda x. lambda y. y)$ reduces to $lambda x. lambda y. y$. Asked By : prerm2686 Answered By : sepp2k The reason Read More …
[Solved]: Has it been proven that the optimization TSP is (or is not) polynomial-time verifiable if P ≠ NP?
Problem Detail: The optimization version of TSP asks for the length of the shortest tour. Unlike the decision version of TSP, there’s no obvious way to verify a proposed solution of the optimization problem in polynomial time. But is there a Read More …