Questions tagged [computer-science]
For question borderline with, or having application to, computer science. Consider also posting http://cs.stackexchange.com/ or http://cstheory.stackexchange.com/ instead of here, if appropriate.
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Guess that group via product queries
Suppose someone (person B) knows a finite group $G$ of order $n$.
You (person A) know only the order $n$,
and that $1$ is the name of the identity element.
The group elements are named $1,2,\ldots,n$ ...
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Can Shor's Algorithm be modified to run efficiently on a classical computer?
Shor's algorithm is an algorithm which factors integers in polynomial time on a quantum computer. If one tries to run it on a classical computer, one runs into the problem that the state vector that ...
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6
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1
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Applications of small Kakeya sets over finite fields
It was proved by Dvir that a Kakeya set in $\mathbb{F}_q^n$ has size at least $q^n/n!$, a bound which was later improved to $q^n/2^n$.
For $n = 2$ and $q$ odd the exact bound is $q(q+1)/2 + (q-1)/2$ ...
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0
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Counting models in first order logics without existencial quantifiers
My question is about the posibility of to construct a parameter space of models in a first order theory, finitely presented, with out existencial quantifiers (parameter space in the sense of ...
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Does Langton's ant cover every n by 6 gridded torus?
This post follows this other post about times cover by Langton's ant of $n$ by $n$ gridded torus.
For $n$ by $n$ gridded torus, I've checked for $n \le 1000$ that the ant covers all. This fact needs ...
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1
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cohomology algebra of submanifold in euclidean space
If we write a manifold or CW-complex $X$ as a subset of $\mathbb{R}^n$, in expression of coordinates, for example, \begin{multline}
F(S^2,k+1)=\{(x_1,x_2,x_3,\cdots, x_{3k+1},x_{3k+2},x_{3k+3})\in\...
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1
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1
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Optimal covering
Let consider a problem of optimal covering of Hamming space.
So we have Hamming space $\{0,1\}^n$ and some integer $r$. We want to find a set $A \subseteq \{0,1\}^n$ such that any point from $\{0,1\...
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0
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Are there any interesting open questions having to do with submodularity, specially in the intersection of theoretical machine learning? [closed]
I was interested in knowing about open research topics related with sub modularity, specially within its intersection with theoretical machine learning (and related topics).
It seems to me that much ...
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Are all $k$th-longest-tour problems equally hard?
It is well known, that determining the shortest and, the longest Hamilton Cycle of a complete graph with real edge weights are algorithmically two sides of the same medal: one transforms to the other ...
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How to calculate the sum of remainders of N?
I'm trying to sum the remainders when dividing N by numbers from $1$ up to $N$
$$\sum_{i = 1}^{N} N \bmod i$$
It's easy to write a program to evaluate the sum if N is small in $O(N)$ but what if N is ...
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2
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Define Turing machine with algebraic concepts/structures
Usually, during lectures Turing Machines are firstly introduced from an informal point of view (for example, in this way) and then their definition is formalized (for example, in this way).
Is it ...
user60665
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1
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Sorting interleaved sorted lists
By interleaving two lists I mean to combine them into a single list in any way that maintains the relative order of the elements coming from each list. For example, interleaving $(x_1,x_2,x_3)$ and $(...
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How to generate $n$ FP32 rationals s.t. no two distinct k-el. subsets have same sum?
First some
Background: I have lots and lots of integer matrices, whose rows are $k$-combinations (without repetitions and sorted) of numbers from the set $S:=\{1,...,n\}$ and needed to be compared ...
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Counting path generating sentences in a specific formal language
Given a formal grammar of a language or an Turing machine of the language, can we count the path that generating sentences of the language?
For example, we know that if the grammar is context-free ...
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2
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Can an algorithm decide whether a program computes all strings? [closed]
I am interested in the type of program, which is given as input to a Universal Turing Machine (UTM) with language $L$, and for which it holds that every possible finite string $s$ of symbols in $L$ ...
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1
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How to formalize "Is there a proof for every instance of the halting problem?"? [closed]
In a previous question that I asked here it turned out that for every instance of the halting problem, being the matter whether a certain computer program halts or runs forever, there exists a ...
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1
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Is there a consistent theory for each instance of the halting problem?
I got a bit confused by a discussion about the provability of the Goldbach conjecture and the seemingly different opinions about this subject. Since I understand computer science better, I will ask my ...
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1
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Concept of synchronizability
This thread is about the concept of synchronizability. It's a concept I tried to formalize in its most general sense but without success. The goal of this thread is therefore to try to formalize it in ...
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Can this way of comparing numbers of the form a+b sqrt(K) be generalized?
So I want to make a system for computing with various classes of numbers. One of those is a class of number closed under the standard arithmetic operators ($+$, $-$, $*$ and $/$) along with square ...
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Reconstructing a string from random samples
What is known about the following problem?
Reconstruct a string $\sigma$ of known length $n$ over a known
alphabet $\Sigma$ from a collection of uniformly and independently
chosen $k$-long ...
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0
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Is there an efficient algorithm for sampling from the negative hypergeometric distribution? [closed]
I'm writing a small statistics library currently. One of the algorithms I'm implementing has two variants: one that samples the hypergeometric distribution and one that samples the negative ...
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When does the greedy change-making algorithm work?
The change-making problem asks how to make a certain sum of money using the fewest coins. With US coins {1, 5, 10, 25}, the greedy algorithm of selecting the ...
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scott continuity, sub additivity
Let $(X, \sqsubseteq_x)$ and $(Y, \sqsubseteq_y)$ be two posets and let $\delta_x:X \to X$ and $\delta_y:Y \to Y$ be two closure operators (monotone, inflationary, idempotent). Then, a monotone ...
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A continuous function for defining unique values to a 1024x1024 image with a 24 bit 3 color channel image
I need to generate a color map which I am not sure exist. I have a 1024x1024 image which would contain 2^20 pixels. I have 3 color channels which each have 8 bits which would leave us with 2^24 ...
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2
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Background for Kierstead terms
I was looking at some slides of John Longley's here, where he mentions "the Kierstead functional"
$$\lambda f.f(\lambda x.f(\lambda y.x)) \ ,$$
(where $f$ should be of type $2$, and $x,y$ of ground ...
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vote
1
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Total conditional complexity
By $C(|)$ denote conditional complexity.
By $CT(|)$ denote total conditional complexity.
For every n there exist two strings $x$ and $y$ of length $n$ such that $C(x|y) = O(1)$
but $CT(x|y) \ge n $.
...
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8
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1
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Compute an arbitrary decimal place of $\pi$
Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?
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AI / Machine Learning related to high/modern/front mathematics [closed]
I major math and cs. and i'm interested in ai/machine learning/data mining.
so i want to know what math subjects are used in frontier of these technology.
especially, high mathematical tool, like ...
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1
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internal language for the 2-category of small categories
What is the internal language of the category Cat of small categories?
I found an article by Glynn Winskel and his student Mario Jose Cáccamo about such calculus! However it is limited to a fragment ...
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1
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A certain instance of the Set Covering problem
Is there any useful structure associated with the following instance of the Set Covering problem?
Let $G$ be a weighted graph and let $\mathcal{P}$ denote the set of all shortest paths between all ...
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1
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How to select a subset of points from a universal to minimize the distance from outside to inside?
Here is the detailed problem.
I have a set of N points in K-dimension space, called U, and I want select M points of them, called S. For each point p in U, we define the distance from p to S as
$$ d(...
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Given a formal power series ,decide whether there exists a polynomial the series satisfies and if it exists,how to write it down?
Given a formal power series $$y(x)=\sum_{i=0}^{\infty} a_i x^i$$ Is there an algorithm that decides whether there exists a polynomial$$ P(x,y)=p_n(x)y^n+p_{n-1}(x)y^{n-1}+\cdots+p_0(x)=0,p_j(x)\in F[x]...
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Which distributions can you sample if you can sample a Gaussian?
Explicitly: You have a computer that is able to pick a real number at random according to the normal distribution: $\mathcal{N}(0,1) = \frac{1}{\sqrt{2\pi}}e^{-x^2/2}$. Which distributions can this ...
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A problem related to routing in a graph
I have come across a new problem - I want to know whether this problem is similar to some existing problem or not.
The new problem is this. There is a tourist who has a having the following ...
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Fast checking that overdetermined polynomial system does not have a solution
As a result of some inductive procedure for each $n$ I have a system of about $n^2$ polynomial equations with $n$ variables with integer coefficients, which can be precisely computed. As the system is ...
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Correspondence between numerical semigroups and polynomials?
A numerical semigroup $A$ is defined as a subsemigroup of the semigroup $(\mathbb{N},+)$ of the positive integers such that the set $\mathbb{N}\setminus A$ is finite. Equivalently (for a subsemigroup) ...
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1
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Connection between inf-entropy rate and min-entropy
I am reading the paper "Generating random bits from an arbitrary source: fundamental limits" by Vembu and Verdu. This paper is written in the language of information theory, however, I need to ...
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Is there an unambiguous CFL whose complement is not context-free?
I'm doing a little bit of research about context-free languages. A question that's popped up is whether or not there exists an unambiguous context-free language whose complement is not a context-free ...
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largest size for a randomness extractor
I am not so expert in theoretical computer science, so sorry if the question is trivial, i just could not find it in literature.
Suppose we have a source $X$ with min-entropy $\ell$, the randomness ...
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Which automated theorem provers can address the combinatorics of periods in strings?
Five years ago, I made a conjecture on the number of correlation classes that are exhibited by pairs of words in an alphabet of a given size. I later speculated that the conjecture could be tackled ...
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Number of partitions whose blocks form arithmetic progressions
As is known, the set $\{1,\ldots,n\}$ has $2^n$ many subsets and $B_n$ (the $n$th Bell number) many partitions, where clearly $B_n<2^{2^n}$ and it is actually known that $B_n<n^n$ for large $n$. ...
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1
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How many edges can you put in a graph such that every edge belongs to a minimal $k$-cycle?
I am trying to solve:
Given $n, k$, find maximum $m$ such that there exists a graph on $n$ nodes, $m$ edges such that every edge is part of a minimal $k$-cycle.
I only care about the asymptotic ...
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1
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Self-similarity in the theory of computability
Let $M = w_0w_1... \in \{0,1\}^*$.
For any computable function $f$ define $M_f = w_{f(0)}w_{f(1)}...$
Let for any computable strictly increasing function $f$ there is continuous
computable mapping ...
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Private Randomness extractor
Suppose we are given two random variables $X$ and $Y$ with fixed marginal and joint distribution. What is the maximum randomness that we can extract from $Y$ that is independent from $X$, that is, if $...
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Wanted: a "Coq for the working mathematician"
Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar with....
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Fundamental Problems in Mathematics that, without Computer Sciences, would not be resolved? [closed]
Could you please give examples of fundamental questions in mathematics (let us say, pure mathematics) which were resolved fundamentally by the use of computers? More precisely, are there examples that ...
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Separating infinite words sharing factors by automata
Two infinite words $\xi, \eta \in X^{\omega}$ are separated by an (Büchi-)automaton if it accepts one but not the other.
Denote by $F_n(\xi)$ the factors of length $n$ of an infinite word $\xi$ and ...
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How feasible is it to prove Kazhdan's property (T) by a computer?
Recently, I have proved that Kazhdan's property (T) is theoretically provable
by computers (arXiv:1312.5431,
explained below), but I'm quite lame with computers and have
no idea what they actually can ...
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7
votes
1
answer
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Generalising the adherence operator and its closure properties with regard to regular (rational) languages
Let $X$ be an alphabet and denote by $X^{\omega}$ the set of all infinite sequences (i.e. words) in $X$. A subset $L \subseteq X^{\omega}$ is called $\omega$-regular if it is acceptable by some Büchi-...
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Subsets of all Diophantine's sets
I have asked this question on math.stackexchange already:
https://math.stackexchange.com/questions/627461/subsets-of-all-diophantines-sets
Function $\mathbb{N}^k \to \mathbb{N}^m$ is computable $\...
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