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Author: ignougroup

Minimum space needed to sort a stream of integers

January 23, 2017March 27, 2017 ignougroup

Problem Detail: This question has gotten a lot of attention on SO: Sorting 1 million 8-digit numbers in 1MB of RAM The problem is to sort a stream of 1 million 8-digit numbers (integers in the range $[0,: 99mathord{,}999mathord{,}999]$) using only Read More …

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Proving a grammar only generates words whose alternating digit sums are multiples of three

January 23, 2017March 27, 2017 ignougroup

Problem Detail: This is homework and I’m looking for a push in the right direction. Proofs were never something I was properly taught, so now they’re kind of a weak point. Here’s the problem: The following grammar generates numbers in binary Read More …

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What randomness really is

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I’m a Computer Science student and am currently enrolled in System Simulation & Modelling course. It involves dealing with everyday systems around us and simulating them in different scenarios by generating random numbers in different distributional curves, like IID, Read More …

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Finding examples of languages that are “anti-palindromic”

January 23, 2017March 27, 2017 ignougroup

Problem Detail: Let $Sigma = { 0, 1 }$. A language $L subseteq Sigma^* $ is said to have the “anti-palindrome” property if for every string $w$ that is a palindrome, $wnotin L$. In addition, for every string $u$ that is Read More …

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Seating Chart Optimization

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I’m trying to find an algorithm to solve the seating chart problem. The goal is to place pepole at one (or multiple) tables such that the overall happiness is maximized. Each seat has neighbors. A person on a seat Read More …

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How to find max number with a single-tape turing machine?

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I’d appreciate hints for this problem I’m trying to design a Turing Machine which calculates $max {x_1, x_2,..,x_k }$. Assuming $1 = 1^1; 2=1^2; n=1^n$ and all numbers/strings are separated by a blank character $B$. Asked By : Iancovici Answered Read More …

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Sub language is not Turing-recognizable, or could it be?

January 23, 2017 ignougroup

Problem Detail: Let A and B be languages with A ⊆ B, and B is Turing-recognizable. Can A be not Turing-recognizable? If so, is there any example? Asked By : Wilhelm Answered By : Kaveh This is something that confuses many students. The Read More …

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What makes PROLOG Turing-complete?

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I know that it can be proven PROLOG is Turing-complete by constructing a program that simulates a Turing machine like this: turing(Tape0, Tape) :- perform(q0, [], Ls, Tape0, Rs), reverse(Ls, Ls1), append(Ls1, Rs, Tape). perform(qf, Ls, Ls, Rs, Rs) Read More …

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Describing a Turing machine that computes $lceillog_{2}(n)rceil$

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I need to describing a Turing machine that computes $lceillog_{2}(n)rceil$ I know that: n = 1, 2, 3, 4, 5, 6, 7, 8, … f(n) = 0, 1, 2, 2, 3, 3, 3, 3, … So I’m thinking of Read More …

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Is radix sort really O(n) for sorting 32 bit integers?

January 23, 2017March 27, 2017 ignougroup

Problem Detail: I was trying to analyze radix sort in terms of time and space. Assume that we are given $n$ 32-bit integers which we would want to sort by looking at the least significant digits first. $k$ is the total Read More …

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