Category: Uncategorized

Problem Detail: Is that statement false or true? I believe it’s false because ln(n) = log base e of n. So therefore, log base 2 of n can be a minimum because in 2^x = n, x will always be less Read More …

Problem Detail: I’m clojure user myself. I’m trying really hard to learn haskell and to better understand the type system. However, I feel that trying to ‘type’ everything is quite restrictive when the problem or the data is less defined. I Read More …

Problem Detail: Given a Turing machine $M$, we say that $L(M) in P$ if the language decided by the machine can be decided by some machine in polynomial time. We say that $M in P$ if the machine runs in polynomial 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 …