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0answers
116 views

If wolfram rule 110 is universal , does it mean it can solve mathematical equations? [on hold]

Stephan wolfram states that Rule 110 in Elementary Cellular Automata is computational universal . Does it mean that it can solve mathematical equations , like the quadritic equations ??? And if it ...
5
votes
2answers
169 views

If $f : [-a,a] \rightarrow \mathbb{IR}$ is Scott continuous, why are $f^-$ and $f^+$ measurable?

In "A domain theoretic account of Picard's theorem" (http://www.doc.ic.ac.uk/~dirk/Publications/icalp2004.pdf), the authors assert the following. Let $\mathbb{IR}$ be the interval domain $\lbrace ...
0
votes
1answer
43 views

Finding t vlaue in Bezier curve [closed]

According to this question, I'm looking for some method to find the t value in Quadratic bezier curve equation: $$ B(t)=P_0+t(1-t)P_1+t^2P_2 \space \space where \space 0 ≤ t ≤ 1 $$ In this ...
0
votes
0answers
21 views

Canonical representation of binary decision trees in Ptime?

I am wondering about the possibility of efficiently (here: in Ptime) representing binary decision trees (BDT) by some other data structure in a way that characterizes their equivalence. More ...
0
votes
0answers
43 views

Finding a movement taking out of a convex set

There is a convex set $S$ as the hull of M points in an D-dimensional Euclidean space and a point $\vec P$ in the set. Then, there is a set of vectors $\vec W$ taking the form $\vec W=\sum_{i=1}^N ...
21
votes
3answers
757 views

What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?

Over the years, advances in machine learning has allowed us to communicate and interact, using the same natural language, more and more semantically with computers, e.g. Google, Siri, Watson, etc. On ...
6
votes
0answers
141 views

Distribution of trivial subset sums

Suppose I have a set $S$ of $n$ integers picked independently, uniformly at random from $[-L, L].$ Let $z(S)$ be the number of subsets of $S$ which sum to zero. The question is: what is the ...
8
votes
3answers
653 views

Why does the bitxor function appear in Nim?

I am conducting research in Combinatorial Game Theory (CGT). Although I have done a considerable amount of reading, I do not completely understand why the bit-xor function also known as the nim-sum ...
5
votes
0answers
168 views

Unique Nash equilibrium games

Multicast network design game is a special case of a general network design game (http://www.cs.cornell.edu/home/kleinber/focs04-game.pdf) in which there is a target vertex $t$ and $n$ rational ...
1
vote
1answer
249 views

Functional programing and intensional type theory

I know very little about how computers work, so please excuse my ignorance! I think of the Glasgow Haskell Compiler as a program that eats up extensional type theory and spits out a program which ...
2
votes
0answers
118 views

Polynomial-time algorithm solving approximately a generalization of the travelling salesman problem

Take a graph $G$ and a number of sets of nodes of $G$. The problem is to find the shortest path passing through at least one node in each node set. If each node set consists of only one node, the ...
-4
votes
1answer
130 views

What exactly is wrong with this statement (Lucas-Penrose fallacy)? [closed]

Statement "For every computer system, there is a sentence which is undecidable for the computer, but the human sees that it is true, therefore proving the sentence via some non-algorithmic method." ...
4
votes
1answer
224 views

Constructing the oracle for Grover's algorithm

For a final project in my class, I decided to try to simulate a quantum computer and implement Grover's algorithm. I followed this excellently written blog post by Craig Gidney, and was successful in ...
5
votes
1answer
133 views

Algorithm that generates a n-simplex that cover n-polytope?

Given an $n$-cube with unit volume, is there any algorithm that generates a $n$-simplex that covers the $n$-polytope?
11
votes
1answer
470 views

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 ...
2
votes
0answers
86 views

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 $q(q+1)/2 + (q-1)/2$ ...
1
vote
0answers
68 views

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 ...
11
votes
0answers
316 views

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 ...
2
votes
1answer
106 views

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, ...
1
vote
1answer
85 views

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 ...
2
votes
0answers
179 views

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 ...
3
votes
1answer
531 views

Mathematics of Computer science and AI [closed]

Computer science and Artificial Intelligence have been fertile grounds for research for decades, not only for Engineers but particularly for Mathematicians. What kinds of Mathematics have emerged ...
3
votes
0answers
68 views

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 ...
4
votes
2answers
740 views

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 large ...
5
votes
2answers
328 views

TM and abstract algebra

Usually, during lectures Turing Machines are firstly introduced from an informal point of view (for example, in this way: http://en.wikipedia.org/wiki/Turing_machine#Informal_description) and then ...
3
votes
1answer
169 views

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 ...
3
votes
1answer
151 views

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 ...
0
votes
0answers
79 views

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 ...
-1
votes
2answers
430 views

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 $L$ ...
0
votes
1answer
236 views

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 ...
0
votes
1answer
211 views

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 ...
0
votes
0answers
158 views

Trilateration issues, when circles don't intersect

I'm working on Indoor localization where I've deployed multiple iBeacons in my environment. I'm taking distances from all the beacons through their RSSI values. They are not 100% accurate though. Now ...
0
votes
0answers
35 views

How can be a conservative field constraint be efficiently implemented in a continuous optimization problem?

Suppose we have the following continuous optimization problem: $$ \underset{x}{\mathrm{minimize}}f\left(x\right) $$ subject to $$ \exists X:\nabla X=Jac\left(X\right)=x $$ where $f$ is a function ...
1
vote
1answer
218 views

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 ...
5
votes
2answers
190 views

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 ...
8
votes
1answer
134 views

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 ...
1
vote
0answers
60 views

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 ...
3
votes
2answers
364 views

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 ...
6
votes
2answers
107 views

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 ...
7
votes
2answers
431 views

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 ...
2
votes
2answers
111 views

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 ...
1
vote
1answer
160 views

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 $. ...
-4
votes
1answer
252 views

An algorithm and symbolic manipulation for IF-THEN-ELSE [closed]

CONCLUSION (so far)  Look at the parentheses theorem and at the comments below the question(s) :-) As for now, only Dan Peterson has truly addressed the issue. Q1   Does there exists an ...
8
votes
1answer
233 views

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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votes
1answer
320 views

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 ...
2
votes
0answers
93 views

Mean Capture time for the Rabbit-Hunter paper by Peres et al [closed]

I am a non-math student. I am trying to read the paper "Hunter, Cauchy Rabbit, and Optimal Kakeya Sets" by Yuval Peres et al. Link - http://arxiv.org/abs/1207.6389 In his video based on the paper - ...
3
votes
1answer
177 views

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 ...
1
vote
1answer
98 views

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 ...
1
vote
1answer
51 views

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 $$ ...
2
votes
2answers
433 views

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 ...