Category: Uncategorized

Problem Detail: I am trying to prove problem 1.59 in Sipser’s book: Introduction to the theory of computation , 2nd Edition. Let $M=(Q,Sigma,delta,q_0,A)$ be a DFA and let $q’$ be a state of $M$ called its “home”. A Synchronizing sequence for Read More …

Problem Detail: I was reading an answer to a recent question, and sort of a strange, ephemeral thought came to mind. My asking this might betray either that my theory chops are seriously lacking (mostly true) or that it’s just too Read More …

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 …

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 …

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 …

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 …

Problem Detail: Suppose we have $N$ fixed points (set $S$ with $|S|=N$) on the plane and $m$ agents with fixed, known initial positions ($m<N$) outside $S$. We should transfer the agents so that in our final configuration they are all positioned Read More …

Problem Detail: If I had a graph $G$ with some negative edge weights, clearly Dijkstra’s algorithm does not definitely halt, since it might get caught in a negative cycle (shedding infinite weight). However, would finding the minimum weight (most negative weight) Read More …

Problem Detail: I came across an issue with the definition of a (directed) graph in Sipser’s Introduction to the theory of computation, 2nd Ed. On pp.10, An undirected graph, or simply a graph, is a set of points with lines connecting Read More …