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1500 questions
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What are potential pitfalls with having a minimal kernel that runs managed code?
Suppose I want to build an operating system based on a very small native lower kernel that acts as a managed code interpreter/runtime and a larger upper kernel compiled to a non-native machine language (Java bytecode, CIL, etc.). Examples of similar…
Adam Maras
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Do non-computable functions grow asymptotically larger?
I read about busy beaver numbers and how they grow asymptotically larger than any computable function. Why is this so? Is it because of the busy beaver function's non-computability? If so, then do all non-computable functions grow asymptotically…
hollow7
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Do computers actually use carry-lookahead adders?
There are plenty of details about carry lookahead adders such as Kogge-Stone, Lander-Fischer, etc. in college CS courses. They are described as "common in the industry". However, I can't find any evidence (aside from maybe the Manchester carry…
qwr
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Why doesn't Knuth's linear-time multiplication algorithm "count"?
The wikipedia page on multiplication algorithms mentions an interesting one by Donald Knuth. Basically, it involves combining fourier-transform multiplication with a precomputed table of logarithmically-sized multiplications. It runs in linear…
Craig Gidney
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When did $LR(k)$ acquire the meaning "left-to-right scan, rightmost derivation?"
According to the Wikipedia article, the L in $LR(k)$ means "left-to-right scan", and the "R" means "rightmost derivation." However, in Knuth's original paper on $LR(k)$ grammars, he defines $LR(k)$ (on page 610) as a language that is "translatable…
templatetypedef
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14
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What does "non-pathological data" mean?
I took an algorithms class on Coursera. The professor in the video about hash tables said that
What's true is that for non-pathological data, you will get constant time operations in a properly implemented hash table.
What does "non-pathological…
Alexander Myshov
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Is there an abstract machine that can capture power consumption?
When reporting algorithmic complexity of an algorithm, one assumes the underlying computations are performed on some abstract machine (e.g. RAM) that approximates a modern CPU. Such models allow us to report time and space complexity of algorithms.…
user20
14
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Expected number of swaps in bubble sort
Given an array $A$ of $N$ integers, each element in the array can be increased by a fixed number $b$ with some probability $p[i]$, $0 \leq i < n$. I have to find the expected number of swaps that will take place to sort the array using bubble…
TheRock
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Computational complexity vs. Chomsky hierarchy
I'm wondering about the relationship between computational complexity and the Chomsky hierarchy, in general.
In particular, if I know that some problem is NP-complete, does it follow that the language of that problem is not context-free?
For…
sjmc
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Complexity of finding the pseudoinverse matrix
How many arithmetic operations are required to find a Moore–Penrose
pseudoinverse
matrix of a arbitrary field?
If the matrix is invertible and complex valued, then it's just the inverse. Finding the inverse takes $O(n^\omega)$ time, where…
Chao Xu
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Why use languages in Complexity theory
I'm just starting to get into the theory of computation, which studies what can be computed, how quickly, using how much memory and with which computational model.
I have a pretty basic question, but am really hoping some of you guys can help me…
Matteo
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Lambda calculus: difference between contexts and evaluation contexts
Firstly, I'd like to say that my text below may contain errors, so feel free to point out any mistakes in my formulation of the question.
Consider an untyped lambda calculus with booleans and if-statements whose terms are given by this syntax:
t…
Squera
14
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Turing machine - infinite tape in one or two directions
I have seen turing machines beeing represented with tapes infinite in one, and in two directions. Is there any difference in the power of such turing machines, or are they basically equivalent? In my head I think they are equivalent, since I guess…
user2795095
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What are the state-of-the-art algorithms for pathfinding on a continuous map of the Earth?
Suppose I have got a solar-powered autonomous surface vessel somewhere in the fjords of Norway, supplied with a fairly recent set of maps, a GPS receiver, and no means of downlinking detailed commands from me. This vessel has to reach, say, the…
Deer Hunter
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Time complexity of base conversion
Why can't arbitrary base conversion be as fast as converting from base $b$ to base $b^k$ ?
Seems to be a big time complexity difference! I am also interested in reading material about it.
Old. Original detailed question
Conversion between…
Hernan_eche
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