Category: Uncategorized

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 …

Problem Detail: Let r be the number of rows in a DRAM array, and c be the number of columns. Apparently, DRAM with organization 16×1 requires least pins when r = c = 4 because fewer address bits are required to Read More …

Problem Detail: From the book The Nature of Computation by Moore and Mertens, exercise 8.9: Consider the problem ACYCLIC GRAPH of telling whether a directed graph is acyclic. Show that the problem is in NL, and then show that the problem Read More …

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 …