Problem Detail: I’m still new to CFG and CNF and have trouble sometimes understanding the concepts. I’m trying to convert this CFG into Chomsky Normal Form: G: S -> aSbS | bSaS | epsilon I think the language generates all strings Read More …
Category: Uncategorized
[Solved]: Vertex cover of a graph by removing leaf-vertices from a DFS tree
Problem Detail: Question taken from “The Algorithm Design Manual” by Steven S. Skiena, 1997. A vertex cover of a graph $G=(V,E)$ is a subset of vertices $V’subseteq V$ such that every edge $ein E$ contains at least one vertex from $V′$. Read More …
[Solved]: Typical file structure
Problem Detail: Short version The question & answers relate to the following topics: File as a collection of records vs. file as a stream of bytes Sequential File Distinction between file data and metadata Transfer of metadata along with the Read More …
[Solved]: Proof: Sum of weights of paths in a network
Problem Detail: I was given problem 6.7 out of the book “Networks: An Introduction” as a question. The problem is defined as follows: Consider the set of all paths from node $s$ to node $t$ on an undirected network with adjacency Read More …
[Solved]: Problem with derivative of sigmoid activation function
Problem Detail: I’m following Jeff heatons book ‘Introduction to Neural Networks with Java’. To get node deltas, we need to calculate $f'(sum)$. In the very first row for Training Element #1, we need to compute $f'(1.13) cdot 0.25$ which Heaton evaluates Read More …
[Solved]: Has this model of random directed graphs been studied?
Problem Detail: Youtube recently added a feature called autoplay, where each clip is assigned a (presumably related) clip that follows it. This, in effect, defines a directed graph on the set of youtube clips, where each vertex has outdegree 1. The Read More …
[Solved]: Knight’s tour from all starting positions
Problem Detail: Is it true that for all $ngeq 5$, there is a knight’s tour of an $ntimes n$ chessboard beginning at every square? For example, is it correct, that there is no solution for a $5times5$ board, with start position Read More …
[Solved]: Prove that languages which contain words whose lengths are multiples of a constant are regular
Problem Detail: This is a problem involving the theory of regular languages. I am stuck on this problem and do not know how to solve this type of problem. Prove that the language $B_n = { a^k mid k text{ is Read More …
[Solved]: Can a solvable problem be encoded in a recursively enumerable language?
Problem Detail: Imagine I have a turing machine that can decide on a specific problem using a language. My question is that that problem (that can be decided by a TM M, with language L) can be encoded in a new Read More …
[Solved]: Hardness of mixed 3-SAT and 2-SAT formula
Problem Detail: It is well known that 3-SAT is $sf NP$-complete , but 2-SAT is in $sf P$. Let there be a formula with $n-1$ clauses with 2 literals each and only 1 clause with 3 literals. We can solve this Read More …
