Problem Detail: I’m trying to understand a proof regarding radix-sort but to no avail. I’ll first write down a brief summary of the proof and then assign some questions which I hope will be clarified enough. Suppose you have an array Read More …
Category: Uncategorized
[Solved]: Weighted Set covering problem with a fixed number of colors
Problem Detail: I have a set of elements U = {1, 2, …. , n} and a set S of k sets whose union form the whole universe. Each of these sets is associated with a cost. I have a fixed Read More …
[Solved]: n log n = c. What are some good approximations of this?
Problem Detail: I am currently looking into Big O notation and computational complexity. Problem 1.1 in CLRS asks what seems a basic question, which is to get an intuition about how different algorithmic complexities grow with the size of the input. Read More …
[Solved]: How is Turing’s Solution to the Halting Problem Not Simply “Failure By Design”?
Problem Detail: I’m having a hard time viewing Turing’s solution to the Halting Problem as a logician, rather than as an engineer. Here is my understanding of the Halting Problem: Let $M$ be the set of all Turing Machines. Let $i$ Read More …
[Solved]: How do I verify that a DFA is equivalent to a NFA?
Problem Detail: I’m learning how to convert NFAs to DFAs and I want to make sure I’m doing it right. Obviously, going back in the other direction isn’t a thing. Does anyone know of an algorithm to check that a DFA Read More …
[Solved]: If a parser can parse a non-deterministic grammar, is the parser non-deterministic?
Problem Detail: I’ve written a recursive-descent parser generator, and I’m trying to classify it (call me a cowboy coder if you must). According to wikipedia, S → 0S0 | 1S1 | ε, which checks for an even-length palindrome, is a non-deterministic Read More …
[Solved]: does every CFL have an ambiguous CFG?
Problem Detail: some questions have been popping up recently on ambiguity in CFLs/CFGs which can have subtleties (eg languages vs grammars & ambiguity vs inherent ambiguity). wikipedia states: Many [context free?] languages admit both ambiguous and unambiguous grammars, while some languages Read More …
[Solved]: Monotone boolean satisfiability with at most k 1s is NP-Complete
Problem Detail: I am to prove that monotone boolean formula satisfiability checking when at most k variables are set to 1 is an NP-Complete problem. Proving that it is in NP is easy, but I’m having difficulty showing that it is Read More …
[Solved]: Proving that directed graph diagnosis is NP-hard
Problem Detail: I have a homework assignment that I’ve been bashing my head against for some time, and I’d appreciate any hints. It is about choosing a known problem, the NP-completeness of which is proven, and constructing a reduction from that Read More …
[Solved]: Bloom filter and perfect hashing
Problem Detail: A Bloom filter uses a hash function to test membership in a given set $S$, by checking if an item is present of not at the specified position. To mitigate the effect of hash collision, multiple functions are used, Read More …
