Problem Detail: From my understanding for a function to be considered Turing-computable the Turing machine which computes it must terminate for all inputs (according to this http://planetmath.org/turingcomputable and various other sources I’ve read). But then doesn’t this mean that all partial Read More …
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[Solved]: Pumping lemma problem – Choosing the right string to pump
Problem Detail: I have a problem finding the right string to pump for the following language: $$L_1 = {a^{p+q}b^rc^sd^{q+r}e^s mid p, q, r, s ge 0}$$ Which string should I choose to pump? The problem is that I don’t know how Read More …
[Solved]: Example of a false proposition when assuming Type : Type
Problem Detail: In Type Theory if one allows Type to be a member of itself, it makes the theory inconsistent. I understand it by analogy to Russel’s paradox in Set Theory, but would prefer to see it done in Type Theory. Read More …
[Solved]: Reduction from partition to multiprocessor scheduling
Problem Detail: I am kind of unsure about a reduction between two problems. Here are the two problems: PARTITION: Instance: A finite set of n positive integers $S= {a_1,a_2,…a_n}$. Question: Can the set $S$ be partitioned into two subsets $S_1$,$S_2$, s.t. Read More …
[Solved]: Proving algorithm for removing nodes from a complete graph with two kinds of edges
Problem Detail: Lets say $G$ is complete undirected graph with a set of edges coloured either black or red. The problem is to find an algorithm answering if it is possible to remove a subset of nodes from $G$ in a Read More …
[Solved]: Turn biased random number generator into uniform
Problem Detail: I’m looking at a problem in the book Introduction to Algorithms by Cormen et al. It says that if we are given a random number generator rand() which satisfies the distribution: $P(X = 0) = p,;;P(X=1)=1-p,;;0<p<1$, then we can Read More …
[Solved]: Reconstructing files from binary
Problem Detail: Popular view tells us that any kind of information is just a collection of bits, that is zeroes and ones placed in a particular order. I was thus having this thought. Suppose that I have some kind of file Read More …
[Solved]: Distributed algorithms – $alpha, beta$ synchronizers
Problem Detail: I experience a difficulty in solving exercises in distributed algorithm. Below is the the exercise I try to solve, it looks like I miss basic idea. Exercise. Consider a 15-processor asynchronous network with processors 0,…,14. The processors constantly run Read More …
[Solved]: Big-O proof for a recurrence relation?
Problem Detail: This question is fairly specific in the manner of steps taken to solve the problem. Given $T(n)=2T(2n/3)+O(n)$ prove that $T(n)=O(n^2)$. So the steps were as follows. We want to prove that $T(n) le cn^2$. $$begin{align*} T(n)&=2T(2n/3)+O(n) &leq 2c(2n/3)^2+an &leq Read More …
[Solved]: What is an edge hop?
Problem Detail: I’ve tried googling it, but found nothing. Here is the context it’s in: From Bayesian Reasoning and Machine Learning: Adjacency matrices may seem wasteful since many of the entries are zero. However, they have a useful property that more Read More …
