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7 answers

Where to find published research papers?

Coming from the POV of someone who is thinking about pursuing a PhD in Computer science. I am having trouble deciding what I would focus my research on when I go for my PhD. See also this question on academia.SE. So I am thinking that…
Taylor Huston
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Finding exact corner solutions to linear programming using interior point methods

The simplex algorithm walks greedily on the corners of a polytope to find the optimal solution to the linear programming problem. As a result, the answer is always a corner of the polytope. Interior point methods walk the inside of the polytope. As…
Jules
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How does a wifi password encrypt data using WEP and WPA?

How does the password that we enter (to connect to a wireless network) encrypt the data on the wireless network? Through my reading I am not sure if the password that we enter is the same as the passphrase. If that is right then how can the…
MR.NASS
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Difference between Turing machine and Universal Turing machine

I've read what a Turing machine and a UTM are, but I don't get the difference. What can a UTM do which a normal Turing machine can not?
Moltimor
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How to convert an NFA with overlapping cycles into a regular expression?

If I understand correctly, NFA have the same expressive power as regular expressions. Often, reading off equivalent regular expressions from NFA is easy: you translate cycles to stars, junctions as alternatives and so on. But what to do in this…
zell
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Example of unrestricted grammar which produces non-context-sensitive language

I'm talking about Type-0 (Chomsky hierarchy) unrestricted grammar, where production rules of grammar are of the form $\alpha\rightarrow\beta$, where $\alpha,\beta\in N\cup\Sigma$. I can not find any example of real unrestricted grammar which…
Andrey Lebedev
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Why is DFS considered to have $O(bm)$ space complexity?

According to these notes, DFS is considered to have $O(bm)$ space complexity, where $b$ is the branching factor of the tree and $m$ is the maximum length of any path in the state space. The same is said in this Wikibook page on Uninformed…
user20691
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3 answers

Modifying Dijkstra's algorithm for edge weights drawn from range $[1,…,K]$

Suppose I have a directed graph with edge weights drawn from range $[1,\dots, K]$ where $K$ is constant. If I'm trying to find the shortest path using Dijkstra's algorithm, how can I modify the algorithm / data structure and improve the time…
user1675999
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Chaitin's constant is normal?

According to this source, Chaitin's constant $\Omega$ is normal. Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Indeed, each halting…
Anon21
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Is packing a bag of presents easier for Rupert than Santa?

Or: Do we need Rupert in order to get presents at all? Routing issues aside, Santa faces the following problem (many, many times over): Given a bag with capacity¹ $C$ and a set of presents $\{p_1, \dots, p_n\}$, each with size $s_i$, he wants to…
Raphael
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Simplest complete combinator basis pair for flat expressions

In Chris Okasaki's paper "Flattening Combinators: Surviving Without Parentheses" he shows that two combinators are both sufficient and necessary as a basis to encode Turing-complete expressions without the need for an application operator or…
user23893
12
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5 answers

How to find the maximal set of elements $S$ of an array such that every element in $S$ is greater than or equal to the cardinality of $S$?

I have an algorithmic problem. Given an array (or a set) $T$ of $n$ nonnegative integers. Find the maximal set $S$ of $T$ such that for all $a\in S$, $a\geqslant |S|$. For example: If $T$=[1, 3, 4, 1, 3, 6], then $S$ can be [3, 3, 6] or [3, 4, 6]…
drzbir
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Trying to understand this Quicksort Correctness proof

This proof is a proof by induction, and goes as follows: P(n) is the assertion that "Quicksort correctly sorts every input array of length n." Base case: every input array of length 1 is already sorted (P(1) holds) Inductive step: fix n => 2. Fix…
FrostyStraw
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Is extensionality for coinductive datatypes consistent with Coq's logic?

Given a coinductive datatype, one can usually (always?) define a bisimulation as the largest equivalence relation over it. I would like to add an axiom stating that if two members of the type are related by the bisimulation, they are equal in the…
Jannis Limperg
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Treewidth of k x k square grid graphs

According to some slides I found on google, the treewidth of any $k \times k$ square grid graph $G$ is $tw(G) = k$. I just started researching about treewidth and tree decomposition, and for the most part it makes sense. However, I am particularly…
saltthehash
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