Problem Detail: I wonder how I can go about proving that if a language L is decidable in o(nlog(n)) then L must be regular. I should probably mention that by “decidable” I mean “being decidable by single-tape deterministic turing machine”. Thanks Read More …
Category: Uncategorized
[Solved]: $mathbf{NC}$ is closed under logspace reductions
Problem Detail: I am trying to solve the question 6.12 in Arora-Barak (Computational Complexity: A modern approach). The question asks you to show that the $mathsf{PATH}$ problem (decide whether a graph $G$ has a path from a given node $s$ to Read More …
[Solved]: Double hashing – probe count probabilities
Problem Detail: From TAoCP, Vol. 3 by Knuth we know that expected (mean) probe counts for hash tables with open adressing and double hashing collision-resolution are: $1 over 1 – alpha$ – for unsuccessful search ${1 over alpha} ln({1 over 1 Read More …
[Solved]: Language independent software libraries
Problem Detail: When trying to decide on the choice of a programming language for a specific task, people will often tell me: “use this language because it has the best library for the type of problems you are addressing”. I would Read More …
[Solved]: Find the centre of a circle given two points lying on it and its radius
Problem Detail: We have been given 2 points on a circle and its radius. Now I want to find out the centre point of such a circle. How can I code this efficiently without solving the quadratic equations? Asked By : Nikunj Read More …
[Solved]: What is the difference between shortest distance and shortest path?
Problem Detail: I am studying graph currently. I found a question, which asks for The List A[] which shows shortest distances between $V$ and every other vertex The List B[] which shows shortest paths between $V$ and every other vertex as Read More …
[Solved]: Lazily computing a random permutation of the positive integers
Problem Detail: Are there any existing efficient algorithms for lazily computing a random permutation of the positive integers in a given range (e.g. the range offered by an unsigned integer type in a CPU)? What I mean is this: An algorithm Read More …
[Solved]: What’s the difference between Adaptive Control and Hierarchical Reinforcement Learning?
Problem Detail: After watching Travis DeWolf presentation on scaling neural computation, I’m a bit confused about the difference between Reinforcement Learning (whether hierarchical or not) and Adaptive Control. They both seem to be exploring environments and minimizing error through learning, but Read More …
[Solved]: Is a balanced binary tree a complete binary tree?
Problem Detail: Considering that the opposite is true it’s not mentioned anything about this. I am assuming its not, but I need a very good distinction between these two types of binary trees. All I know is this: A binary tree Read More …
[Solved]: NSPACE for checking if two graphs are isomorphic
Problem Detail: I was studying nondeterministic Turing Machines and came across the following question: Describe a nondeterministic Turing Machine (NTM) that only accepts two graphs (G1 and G2) if they are isomorphic, and provide the NSPACE. The NTM should use as Read More …
