Problem Detail: A multiplication table is symmetric over a diagonal, so only about $n^2/2$ of the elements in an $n times n$ multiplication table contain unique information. Same goes for addition tables. In fact, the same is true for any table Read More …
Category: Uncategorized
[Solved]: Is path induction constructive?
Problem Detail: I’m reading through the HoTT book and I have a hard time with path induction. When I look at the type in the section 1.12.1: $$text{ind}_{=_A}:prod_{C:prodlimits_{x,y:A}(x=_Ay)to mathcal{U}} left( left(prod_{x:A}C(x,x,text{refl}_x)right) to prod_{x,y:A}prod_{p:x=_Ay} C(x,y,p) right),$$ I have no issue understanding what Read More …
[Solved]: How can an extended linearizable history G be equivalent to sequential history S?
Problem Detail: I am undertaking a module in Concurrent Programming where some of the new content this year covers linearizability, the Java Memory Model, and sequential consistency. Our class slides are companion slides to The Art Of Multiprocessor Programming. I have Read More …
[Solved]: Number of Combinations of Connected Bipartite Graphs
Problem Detail: Given two sets of vertices $U$ (size $n$) and $V$ (size $m$), how many possibilities of set of edges $E$ exist that make the bipartite graph $G = (U, V, E)$ connected? Obviously there are $2^{n m}$ different set Read More …
[Solved]: Can a computer count to infinity?
Problem Detail: So, could a computer count to infinity assuming it was a super computer and had near unlimited amounts of ram and hard drive/solid state drive storage? I am being serious when I ask this. [This is what I am Read More …
[Solved]: How does the Sutherland-Hodgman Algorithm work?
Problem Detail: The following are the Pages-96 and Page-97 of the book Schaum’s outline series of Computer Graphics. The algorithm considers several things: (1) Whether the polygon is Convex or Concave. (2) Whether the polygon is positively or negatively oriented. (3) Read More …
[Solved]: Parikh’s Theorem: CFL’s “contain” regular languages?
Problem Detail: The first sentence of the Wikipedia article for Parikh’s Theorem states: “Parikh’s theorem in theoretical computer science says that if one looks only at the relative number of occurrences of terminal symbols in a context-free language, without regard to Read More …
[Solved]: Minimal basis for set of binary vectors using XOR
Problem Detail: I would be surprised if this isn’t a well-studied problem, but I’m not sure what else to search for at this point: you’re given a set of binary $n$-vectors $S subset {0,1}^n$. The problem is to find another set Read More …
[Solved]: Shortest path that visits maximum number of strongly connected components
Problem Detail: Consider a directed graph. I need to find a path that visits maximum number of strongly connected components in that graph. If there are several such paths the desired path is the path that visits minimum number of nodes Read More …
[Solved]: Is it decidable whether a given context free grammar generates an infinite number of strings?
Problem Detail: Is the decision problem “Does a given context free grammar generate an infinite number of strings” decidable? In order to test whether a context free grammar generates an infinite number of strings or not, we can write a program Read More …
