Problem Detail: The standard way of simulating an NFA on a computer (for implementing regex engines etc) is to construct a DFA that accepts the same language. Otherwise you get problems like exponential blowup. However, for my purpose I need to Read More …
Blog
[Solved]: Why aren’t we researching more towards compile time guarantees?
Problem Detail: I love all that is compile time and I love the idea that once you compile a program a lot of guarantees are made about it’s execution. Generally speaking a static type system (Haskell, C++, …) seems to give Read More …
[Solved]: How exactly do you calculate the hidden layer gradients in the backpropagation algorithm?
Problem Detail: I have been going through the description of the backpropagation algorithm found here. and I am having a bit of trouble getting my head around some of the linear algebra. Say I have a final output layer $L$ consisting Read More …
[Solved]: Proving a Language is Irregular using Myhill-Nerode
Problem Detail: I’m trying to prove that the language: begin{equation*} L = { w in { 0, 1 }^* : w text{ contains more 0’s than 1’s} } end{equation*} is irregular using the Myhill-Nerode theorem. I’ve been through all the basic Read More …
[Solved]: Why not relax only edges in Q in Dijkstra’s algorithm?
Problem Detail: Can someone tell me why almost in every book/website/paper authors use the following: foreach vertex v in Adjacent(u) relax(u,v) when relaxing the edges, instead of: foreach vertex v in Adjacent(u) if (v is in Q) relax(u,v) This is extremely Read More …
[Solved]: Pumping lemma for Context-Free Languages
Problem Detail: I have a question about a specific pumping lemma problem for Context-Free Languages. Suppose we have the following Language: $L = {a^{i}b^{j}c^{k}d^{l} mid 0 < i < k wedge j > l > 0 }$ Here is my attemp Read More …
[Solved]: Turing machine working only with 1’s and blanks – how to encode input?
Problem Detail: Let’s say we have a Turing machine which head can only write 1 or blank to the tape (although it can read all symbols from any input alphabet correctly). Can we operate with it on any input? My approach Read More …
[Solved]: Understanding Tiernan’s Algorithm
Problem Detail: I am currently working through Tiernan’s paper, “An efficient search algorithm to find the elementary circuits of a graph” (published 1970), and I am stuck on point 3 of the following excerpt: The algorithm is named EC for “elementary Read More …
[Solved]: Why is the counting variant of a hard decision problem not automatically hard?
Problem Detail: It is well-known that 2-SAT is in P. However, it seems quite interesting that counting the number of solutions to a given 2-SAT formula, i.e., #2-SAT is #P-hard. That is, we have an example of a problem for which Read More …
[Solved]: What is the complexity of multiplying a matrix by a scalar?
Problem Detail: I would like to know the complexity of multiplying a matrix of $ntimes m$ size by a scalar $alpha$? In fact, I have a directed graph $G=(V,E)$ represented by an incidence matrix $M$. I would like to calculate the Read More …
