Problem Detail: I’m having a lot of trouble constructing a PDA for the language: begin{equation*} {a^m b^n : m < 2n < 3m } end{equation*} I know if I push a symbol for each $a$ I see, then pop 2 symbols Read More …
Blog
Rectangle Coverage by Sweep Line
Problem Detail: I am given an exercise unfortunately I didn’t succeed by myself. There is a set of rectangles $R_{1}..R_{n}$ and a rectangle $R_{0}$. Using plane sweeping algorithm determine if $R_{0}$ is completely covered by the set of $R_{1}..R_{n}$. For more Read More …
Why is non-determinism useful concept?
Problem Detail: An automaton is an abstract model of a digital computer. Digital computers are completely deterministic; their state at any time is uniquely predictable from the input and the initial state. When we are trying to model real systems, why Read More …
How can I academically say that ‘one computer is slower than the other’?
Problem Detail: I’m writing a research paper and I have to basically say that one microcontroller is slower than an other microprocessor. However, I’m worried that simply saying that it’s ‘slower’ wouldn’t be appropriate in a research paper. Am I right? Read More …
Using Amdahl’s law how do you determine execution time after an improvement?
Problem Detail: Speeding up a new floating-point unit by 2 slows down data cache accesses by a factor of 2/3 (or a 1.5 slowdown for data caches). If old FP unit took 20% of program’s execution time and data cache accesses Read More …
Using induction to prove a big O notation
Problem Detail: I’m trying to prove that the following recurrence relation has a runtime of O(n): fac(0) = 1 fac(n+1) = (n + 1) * fac(n) I think that I can use induction in the following manner: Base case If n=0 Read More …
How does this Turing machine accept $a^n b^n$?
Problem Detail: I’m reading this tutorial from the University of Illinois about Turing Machines, and I don’t understand something. They give a pseudocode algorithm for an machine that accepts strings from the language $L = {0^n1^n}$ and a diagram of the Read More …
How to prove a problem is NOT NP-Complete?
Problem Detail: Is there any general technique for proving a problem NOT being NP-Complete? I got this question on the exam that asked me to show whether some problem (see below) is NP-Complete. I could not think of any real solution, Read More …
Counting and finding all perfect/maximum matchings in general graphs
Problem Detail: Recently i’ve been dealing with a problem that led me to the following questions: Is there a good algorithm to enumerate all maximum/perfect matchings in a general graph? Is there a good algorithm for finding all maximum/perfect matchings in Read More …
What is meant by “solvable by non deterministic algorithm in polynomial time”
Problem Detail: In many textbooks NP problems are defined as: Set of all decision problems solvable by non deterministic algorithms in polynomial time I couldn’t understand the part “solvable by non deterministic algorithms”. Could anyone please explain that? Asked By : user5507 Read More …
