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 …
Category: Uncategorized
[Solved]: Complexity of deciding if a formula has exactly 1 satisfying assignment
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 …
[Solved]: Randomized Rounding of Solutions to Linear Programs
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 …
[Solved]: Is Hidoku NP complete?
Problem Detail: A Hidoku is a $n times n$ grid with some pre-filled integers from 1 to $n^2$. The goal is to find a path of successive integers (from 1 to $n^2$) in the grid. More concrete, each cell of the Read More …
[Solved]: Bound on space for selection algorithm?
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 …
[Solved]: Common Algorithms without Asymptotically Tight Bounds
Problem Detail: I can think of functions such as $n^2 sin^2 n$ that don’t have asymptotically tight bounds, but are there actually common algorithms in computer science that don’t have asymptotically tight bounds on their worst case running times? Asked By Read More …
[Solved]: If all infinite r.e. languages have an infinite recursive subset, then do co-r.e. languages not have such subsets?
Problem Detail: If all infinite r.e. languages have an infinite recursive subset, then can we logically take co-r.e. languages to not have such subsets by complemence? Asked By : user2896468 Answered By : Yuval Filmus In one word: no. It doesn’t follow logically. Read More …
[Solved]: Floating point rounding
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 …
[Solved]: Solve Integer Factoring in randomized polynomial time with an oracle for square root modulo $n$
Problem Detail: I’m trying to solve exercise 6.5 on page 309 from Richard Crandall’s “Prime numbers – A computational perspective”. It basically asks for an algorithm to factor integers in randomized polynomial time given an oracle for taking square roots modulo Read More …
[Solved]: Is this an instance of a well-known problem?
Problem Detail: Context I am developing an application and came across a problem that seemed difficult to solve. Before attempting to reinvent the wheel (and trying to solve an NP complete problem on my own), I would like to get Read More …
