Problem Detail: Sorry for layman’s term question, my background in computer science is weak. What I have is a list of shelves with books of varying height. Each shelf stores a value that describes how many shelves (of that height) can Read More …
Category: Uncategorized
[Solved]: Concrete understanding of difference between PP and BPP definitions
Problem Detail: I am confused about how PP and BPP are defined. Let us assume $chi$ is the characteristic function for a language $mathcal{L}$. M be the probabilistic Turing Machine. Are the following definitions correct: $BPP ={mathcal{L} :Pr[chi(x) ne M(x)] geq Read More …
[Solved]: Why does this pumping lemma application “prove” that 0*1* is not regular?
Problem Detail: Here is a proof that $0^*1^*$ is not regular, even though it is regular. I’m having a hard time figuring out what is wrong with the proof. Assume $0^*1^*$ is regular. Let $p$ be the pumping length as defined Read More …
[Solved]: What is the relation between First Order Logic and First Order Theory?
Problem Detail: I thought that any FOT is a subset of FOL, but that does not seem to be the case, because FOL is complete (every formula is either valid or invalid), while some FOT (like linear integer arithmetic) is not Read More …
[Solved]: A heuristic for finding a maximum disjoint set
Problem Detail: Background I need to find a largest set of non-overlapping axis-parallel squares, out of a given collection of candidate squares. This problem is NP-complete. Many papers suggest approximation algorithms (see Maximum Disjoint Set in Wikipedia), but I need an Read More …
[Solved]: How does one formulate a backtracking algorithm
Problem Detail: I am new to learning algorithms. I was reading backtracking algorithm for generating all strings for n bits. If I dry run the program I know the program is giving right result. But I didn’t understood the logic can Read More …
[Solved]: Why is a deterministic Turing machine a special case of a probabilistic Turing machine?
Problem Detail: I have no formal training in computer science as I have not yet taken any such classes, so perhaps this question appears naive. I was reading about BPP and it was claimed that a deterministic Turing machine is a Read More …
[Solved]: Find maximum distance between elements given constraints on some
Problem Detail: I have a list of numbered elements 1 to N that fit into positions on a number line starting with 1. I also have constraints for these elements: The element 1 is in position 1, and element N must Read More …
[Solved]: Negation of nested quantifiers
Problem Detail: The problem is: $$exists x forall y (x ge y)$$ With a domain of all real positive integers. The negation is: $$forall x exists y (x < y)$$ so, if $y = x + 1$, the negation is true. Read More …
[Solved]: How many shortest distances change when adding an edge to a graph?
Problem Detail: Let $G=(V,E)$ be some complete, weighted, undirected graph. We construct a second graph $G'=(V, E')$ by adding edges one by one from $E$ to $E'$. We add $Theta(|V|)$ edges to $G'$ in total. Every time we add one edge Read More …
