Problem Detail: I am following “Introduction to the theory of computation” by Sipser. My question is about relationship of different classes which is present in Chapter 8.2. The Class PSPACE. $P subseteq NP subseteq PSPACE = NPSPACE subseteq EXPTIME$ I am Read More …
Category: Uncategorized
[Solved]: Use closure properties to transform languages to $L := { a^nb^n : nin mathbb N }$
Problem Detail: For the purpose of proving that they are not regular, what closure properties can I use to transform the languages $L_a = { a^*cw mid w in {a,b }^* land |w|_a = |w|_b }$ and $L_b = {ab^{i_1}ab^{i_2}ldots ab^{i_n} Read More …
[Solved]: MST with half the edges the maximum weight
Problem Detail: I have been cracking my head over the following question – You are given an undirected connected graph with an even number of edges. Half of the edges have weight less than C (possibly with repetitions), and the other Read More …
[Solved]: Number of winning combination in Nim
Problem Detail: I am studying game theory and I am wondering how many winning combinations are possible for Nim game? Suppose, stones = 500 and piles = 5. With these number, there are many initial game positions are possible. like [1, Read More …
[Solved]: Z-score relations to perceptrons
Problem Detail: I am learning about preceptrons and my professor noted that z-scores are a commmon pre-processing step to normalizing input variables. Following this, I am having trouble understanding why z-scores are useful when training a preceptron? My current understanding is Read More …
[Solved]: 1-to-1 cryptographically secure bit shuffling
Problem Detail: Given an input item (N bytes), I’m looking for a function that will map this to an output (still N bytes). The function should have the following qualities: It should be 1-to-1 so that all inputs map to some Read More …
[Solved]: How to draw a graph to disprove this statement?
Problem Detail: The Problem: Indicate whether the following statements are true or false: a. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum spanning tree of the graph. b. Read More …
[Solved]: Proof of equivalence of parse-trees and derivations
Problem Detail: Intuitively, every derivation in a context-free grammar corresponds to a parse-tree and vise versa. Is this intuition correct? If so how can I formalize and prove such a thing? Asked By : saadtaame Answered By : saadtaame Theorem. Let $G = Read More …
[Solved]: Equality of NSpace and coNSpace classes
Problem Detail: I’m trying to decide which of the following statements are true: $mathsf{NSpace}(log log n) = mathsf{coNSpace}(log log n )$ $mathsf{NSpace}(lg^2n) = mathsf{coNSpace}(lg^2n)$ $mathsf{NSpace}(sqrt n) = mathsf{coNSpace}(sqrt n)$ I thought immediately that (1) is correct since $lg lg n < Read More …
[Solved]: What is a Turing Machine in class coNP
Problem Detail: On the wikipedia article about the polynomial hierarchy http://en.wikipedia.org/wiki/Polynomial_hierarchy it says “$A^B$ is the set of decision problems solvable by a Turing machine in class A augmented by an oracle for some complete problem in class B” What is Read More …
