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1500 questions
12
votes
1 answer
Reductions among Undecidable Problems
Im sorry if this question has some trivial answer which I am missing. Whenever I study some problem which has been proven undecidable, I observe that the proof relies on a reduction to another problem which has been proven to be undecidable. I…
swarnim_narayan
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12
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3 answers
What is meant by an oracle separation between classes $\mathsf{BPP}$ and $\mathsf{BQP}$?
In these notes about quantum computation by Scott Aronson, he explains that the computation classes $\mathsf{BPP}$ is contained in $\mathsf{BQP}$, but that they are not equal, and
So, the bottom line is that we get a problem -- Simon's problem --…
Mozibur Ullah
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12
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1 answer
Counting number of sums from contiguous subarrays of an array
We are given an array $a[1 \ldots n]$ with all $a[i]>0$.
Now we need to find how many distinct sums can be formed from its subarrays (where a subarray is a contiguous range of the array, i.e., $a[j\ldots k]$ for some $j,k$, the sum is the sum of all…
Salena
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12
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1 answer
Are NP problems lower bounded by exponential order of growth?
My understanding of P. vs NP is quite limited. I can understand P refers to an algorithm with an upper bound (big O) with order of growth $n^c$ for some constant c and variable n. My question is, do NP problems have a hypothesized lower bound order…
user4779
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12
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4 answers
Are there competitions for integer programming?
Are there competitions for integer programming like there are for SAT and MAXSAT?
Omar Shehab
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12
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2 answers
Is there a formal CS definition of VCS and file versions?
I don't know whether it was a joke, but once I read what was referred to as a formal definition of a file in a versioning system such as git, hg or svn. It was something like a mathematical object like a homeomorphism. Was that a joke or is there…
Niklas Rosencrantz
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12
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5 answers
Does it make sense to say Big Theta of 1? Or should we just use Big O?
Does saying $f(x) = \Theta(1)$ provide any extra information over saying $f(x) = O(1)$?
Intuitively, nothing grows more slowly than a constant, so there should be no extra information in specifying Big Theta over Big O in this case.
MattCochrane
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12
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3 answers
Minimum circles to cover a set of points and avoid another set of points
Points are in 2d euclidean space. Given a set of n points, A, and a set of m points, B, what is the minimally sized set of circles such that this set of circles covers all points in A and no point in B is covered by a circle?
circles can have…
user3494047
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12
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2 answers
How to deal with arrays during Hoare-style correctness proofs
In the discussion around this question, Gilles mentions correctly that any correctness proof of an algorithm that uses arrays has to prove that there are no out-of-bounds array accesses; depending on the runtime model, this would cause a runtime…
Raphael
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12
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1 answer
Is the 0-1 Knapsack problem where value equals weight NP-complete?
I have a problem which I suspect is NP-complete. It is easy to prove that it is NP. My current train of thought revolves around using a reduction from knapsack but it would result in instances of 0-1-Knapsack with the value of every item being equal…
Zeta Two
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12
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3 answers
Correctness of Strongly Connected Components algorithm for a directed graph
I have been reading up on algorithm for finding the strongly connected components in a directed graph $G=(V,E)$. It considers two DFS search and the second step is transposing the original graph $G^T$.
The algorithm is the following :
Execute DFS…
Geek
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12
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4 answers
Can an FSA count?
This may be a silly question. It seem clear that an FSA, since it is finite, can only count the number of symbols in its input string up to a number bounded by the number of its states. But now suppose we equip the FSA with output (e.g. printing)…
Torbjörn
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12
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1 answer
How to detect sunshine on a photo
How would you algorithmically detect for any given photo whether the sun was shining when the picture was taken?
Examples
A sample from this webcam at a mountain top:
Clearly the sun is shining.
In this other sample it's far less obvious:
One…
Marcel Stör
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12
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5 answers
Is there any use case for the bottom type as a function parameter type?
If a function has return type of ⊥ (bottom type), that means it never returns. It can for example exit or throw, both fairly ordinary situations.
Presumably if a function had a parameter of type ⊥ it could never (safely) be called. Are there ever…
bdsl
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12
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1 answer
A pumping lemma for deterministic context-free languages?
The pumping lemma for regular languages can be used to prove that certain languages are not regular, and the pumping lemma for context-free languages (along with Ogden's lemma) can be used to prove that certain languages are not context-free.
Is…
templatetypedef
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