Problem Detail: What does a dot (.) mean in predicates? $forall a in A. exists d in D. H(a,d)$ Especially, how is the above different to $ exists d in D. forall a in A. H(a,d)$ I’ve never seen this used Read More …
Category: Uncategorized
[Solved]: Is it possible to do Dependent Types in Typed Racket?
Problem Detail: Is it possible to use Dependent Types in the existing Typed Racket implementation? (ie do they exist in it?) Is it reasonably possible to implement a Dependent Types System using Typed Racket? Asked By : hawkeye Answered By : hawkeye Dependent Read More …
[Solved]: Proving the language $L= {0^n 1^m space | space m equiv 0 space mod space n, space n geq 2 }$ is not regular using the pumping lemma
Problem Detail: I am trying to learn about applying the pumping lemma and I’m not really sure how to go about proving this language isn’t regular with the pumping lemma: $L= {0^n 1^m space | space m equiv 0 space mod Read More …
[Solved]: Constructing Tree (forest) from Ancestor function
Problem Detail: Question: Suppose I have a set of male people, and a function isAncestor(person1,person2) that checks whether person1 is an ancestor of person2 in O(1) time. Eg, isAncestor(grandfather, grandson) would return true. What are some fast algorithms for constructing a Read More …
[Solved]: What is the most efficient algorithm and data structure for maintaining connected component information on a dynamic graph?
Problem Detail: Say I have an undirected finite sparse graph, and need to be able to run the following queries efficiently: $IsConnected(N_1, N_2)$ – returns $T$ if there is a path between $N_1$ and $N_2$, otherwise $F$ $ConnectedNodes(N)$ – returns the Read More …
[Solved]: What is the use of finding minimum number of straight lines to cover a set of points?
Problem Detail: There is that popular problem [1] [2] in the computer science that is finding minimum number of straight lines that covers a given set of points in 2D. Even though I have scanned many papers, none of them has Read More …
[Solved]: Equivalence of Turing Machines
Problem Detail: Consider the following two arguments “For every non deterministic TM M1 there exists an equivalent deterministic machine M2 recognizing the same language.“ “Equivalence of two Turing Machines is undecidable” These two arguments seem a bit contradicting to me. What Read More …
[Solved]: Are there any problems that are easy to compute but hard to verify?
Problem Detail: Assuming P $neq$ NP, NP-complete problems are “hard to solve, but have answers that are easy to check.” Does it make any sense to consider the opposite, that is, problems for which it’s easy to compute a correct answer, Read More …
[Solved]: number of edges in a graph
Problem Detail: I got a problem related to graph theory – Consider an undirected graph ܩ where self-loops are not allowed. The vertex set of G is {(i,j):1<=i,j <=12}. There is an edge between (a, b) and (c, d) if |a-c|<=1 Read More …
[Solved]: Why are regular expressions defined with union, concatenation and star operations?
Problem Detail: A regular expresssion is defined recursively as $a$ for some $a in Sigma$ is a regular expression, $varepsilon$ is a regular expression, $emptyset$ is a regular expression, $(R_1 cup R_2)$ where $R_1$ and $R_2$ are regular expressions is a Read More …
