Author: ignougroup

Problem Detail: In an assignment I’ve been asked to find a CFG for $a^x b^y a^z b^w$, where, $x,y,z,w in mathbb{N}^+$, $y > x$, $z > w$, and $x+z = y+w$. A hint was given, think of the language as $(a^p Read More …

Problem Detail: BACKGROUND: Recently I tried to solve a certain difficult problem that gets as input an array of $n$ numbers. For $n=3$, the only solution I could find was to have a different treatment for each of the $n!=6$ orderings Read More …

Problem Detail: Suppose you had a set $P$ of people. Every person $p_j in P$ is familiar with atleast one other person $p_i$ (familiarity is symmetric). Is there a subset $S$ of people such that for $|S| ge k$, no two Read More …

Problem Detail: One way of looking at regular expressions is as a constructive proof of the following fact: it’s possible to construct the regular languages by starting with a small set of languages and combining them via a small, fixed set Read More …

Problem Detail: The decision problem Given a Boolean formula $phi$, does $phi$ have exactly one satisfying assignment? can be seen to be in $Delta_2$, $mathsf{UP}$-hard and $mathsf{coNP}$-hard. Is anything more known about its complexity? Asked By : sdcvvc Answered By : Juho Your Read More …

Problem Detail: Integer linear programming (ILP) is an incredibly powerful tool in combinatorial optimization. If we can formulate some problem as an instance of an ILP then solvers are guaranteed to find the global optimum. However, enforcing integral solutions has runtime Read More …

Problem Detail: There is a well known worst case $O(n)$ selection algorithm to find the $k$’th largest element in an array of integers. It uses a median-of-medians approach to find a good enough pivot, partitions the input array in place and Read More …

Problem Detail: This is inspired by an interview question. We are given an array of integers $a_1, dots, a_n$ and have to determine if there are distinct $i lt j lt k$ such that $a_k – a_j = a_j – a_i$ Read More …

Problem Detail: Can an IEEE-754 floating point number < 1 (i.e. generated with a random number generator which generates a number >= 0.0 and < 1.0) ever be multiplied by some integer (in floating point form) to get a number equal Read More …