Problem Detail: Prove that $L_1$ is regular if $L_2$, $L_1L_2$, $L_2L_1$ are regular. These are the things that I would use to start. As $L_1L_2$ is regular, then the homomorphism $h(L_1L_2)$ is regular. Let $h(L_1) = L_2$ and $h(L_2) = L_1$, Read More …
Author: ignougroup
[Solved]: Largest reported speedup for a parallel computation?
Problem Detail: A parallel implementation of a computation is usually compared to a sequential version of the same computation. The ratio of the time taken by the sequential version to the time taken by the parallel version is called the speedup. Read More …
[Solved]: Myhill-Nerode style characterization of CFL?
Problem Detail: Define the Nerode equivalence over a language $L subseteq Sigma^{*}$ as $u sim_L v$ iff $uw in L Leftrightarrow vw in L$ for every $w in Sigma^{*}$. The Nerode equivalence ${sim}_L$ has finitely many equivalence classes precisely when $L$ Read More …
[Solved]: naive convex hull algorithms
Problem Detail: I already understood how the well-known algorithms like Graham, Quickhull etc. work, but i have difficulties in understanding 2 naive versions of convex hull algorithms: Let S={p1, …, pn} a set of points and CH(S) the convex hull of Read More …
[Solved]: Why can’t we use a hash tables for collision resolving in hash tables?
Problem Detail: To prevent collisions, hash tables with open addressing use a methodology to chain the contents. Why can’t we use another hash table allocated to each slot of the primary hash table? Asked By : user1675999 Answered By : jbapple The method Read More …
[Solved]: Algorithmic consequences of algebraic formula for partition function?
Problem Detail: Bruinier and Ono have found an algebraic formula for the partition function, which was widely reported to be a breakthrough. I am unable to understand the paper, but does it have any algorithmic consequences for fast computation of the Read More …
[Solved]: ML functions from polymorphic lists to polymorphic lists
Problem Detail: I’m learning programming in ML (OCaml), and earlier I asked about ML functions of type ‘a -> ‘b. Now I’ve been experimenting a bit with functions of type ‘a list -> ‘b list. There are some obvious simple examples: Read More …
[Solved]: Good snapshottable data structure for an in-memory index
Problem Detail: I’m designing an in-memory object database for a very specific use case. It is single writer, but must support efficient concurrent reads. Reads must be isolated. There is no query language, the database only supports: get object/-s by attribute/set Read More …
[Solved]: A partition algorithm
Problem Detail: I have encountered the following problem that I found very interesting to solve: Given an array of positive integers ${a_1, a_2, …, a_n}$ you are required to partition the array into $3$ blocks/partitions such that the maximum of sums Read More …
[Solved]: Correctness of the greedy algorithm
Problem Detail: I am trying to solve the following problem: Given a matrix which consists of only 0’s and 1’s. Considering the matrix as a metal sheet, we need to “cut-out” square blocks of sizes 2×2 consisting of only 0’s from Read More …
