Author: ignougroup

Problem Detail: Let $Sigma$ be the set of terminal and $N$ the set of non-terminal symbols of some context-free grammar $G$. Say I have a string $a in (Sigma cup N)^+$ such that $x a y in mathcal{S}(G)$ where $x,yin (Sigma Read More …

Problem Detail: Can every linear grammar be converted to a linear Greibach normal form, a form in which all productions look like $A rightarrow ax$ where $a in T$ and $x in V cup {lambda}$? ($T$ is the set of terminals, Read More …

Problem Detail: In the step of removing unit productions when converting a grammar to Chomsky normal form, I sometimes found that the variables may end up having the same production bodies. Is this possible? If so, can we consider these variables Read More …

Problem Detail: I read that most scientists don’t believe that P=NP. It might be subjective but can you simplify why not? I’m not informed enough to have an opinion but I’d like to know the definitions and some “pretty simple” explanation Read More …

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 …

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 …

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 …

Problem Detail: Just as a background, 3-colorable problem is as follows: Given a graph $G = (V, E)$, is it possible to color the vertices using just 3 colors such that no neighboring vertices have the same color? I’m aware we Read More …

Problem Detail: How is it possible to print all patterns, of length k, contained in a string using FM-index and burrows-wheeler transform? PROBLEM DETAIL: I think it’s better to leave more details regarding my problem. The input i have are: the Read More …

Problem Detail: Given two languages $L_1$ and $L_2$ that are in $mathsf{P}$, can it be proven that there is a polynomial time reduction from $L_1$ to $L_2$ and vice versa? If so, how? I noticed that if $L_1$ is the empty Read More …