Problem Detail: I am new to this topic, Linear Time Temporal Logic and I am trying to prove this equivalence — $BoxDiamond f Leftrightarrow DiamondBox f$ This is my take — Basic definitions: $(sigma, j) models Box f: forall k , Read More …
Author: ignougroup
[Solved]: Can we create binomial heaps in linear time?
Problem Detail: I’m studying binomial heaps in anticipation for my finals and the CLRS book tells me that insertion in a binomial heap takes $Theta(log n)$ time. So given an array of numbers it would take $Theta(nlog n)$ time to convert Read More …
[Solved]: Why is there readonly (const) in C++, but not writeonly (sink)?
Problem Detail: C++ initially had “readonly” and “writeonly” qualifiers, before “readonly” was renamed to “const”, and “writeonly” removed. My question is: What are the problems with “writeonly” (or a “sink” qualifier)? There are (non-object oriented) programming languages with “in”, “out” and Read More …
[Solved]: Dijkstra’s Algorithm with different color nodes
Problem Detail: You are given a directed graph G = (V, E) and nodes s, t. Nodes are colored red, white, and blue. A path from s to t is called colorful if it contains both a red node and a Read More …
[Solved]: Difference between “data dependence graph”, “data dependency graph”, and “data flow graph”
Problem Detail: Is there a difference between a “data dependence graph” and a “data dependency graph”? I have seen both terms – sometimes used interchangeably sometimes not. To make things even more complicated, a “data dependency graph” is sometimes also called Read More …
[Solved]: How can I show that the Cook-Levin theorem does not relativize?
Problem Detail: The following is an exercise which I am stuck at ( source: Sanjeev Arora and Boaz Barak; its not homework ) : Show that there is an oracle $A$ and a language $L in NP^A$ such that $L$ is Read More …
[Solved]: Connection between NAND gates and Turing completeness
Problem Detail: I know that NAND gates can be used to create circuits that implement every truth table, and modern computers are built up of NAND gates. What is the theoretical link between NAND gates and Turing completeness? It seems to Read More …
[Solved]: Space complexity of directed and undirected graph
Problem Detail: I have started reading graph theory from Introduction to Algorithm. The author starts by saying that if the graph is dense then: $$|E|text{ close to }|V|^2$$ else if the graph is sparse then: $$|E|text{ is much less than }|V^2|$$ Read More …
[Solved]: What is the name of this logistic variant of TSP?
Problem Detail: I have a logistic problem that can be seen as a variant of $text{TSP}$. It is so natural, I’m sure it has been studied in Operations research or something similar. Here’s one way of looking at the problem. I Read More …
[Solved]: Describe in English the pattern in the following regular expressions
Problem Detail: Describe (in English phrases) the languages associated with the following regular expression. it says to be as simple as possible #1 (x (yyy + x)*)* #2 (c (cc)*d(dd)*)* for number 1 I got all words in which when y Read More …
