**-1**

votes

**2**answers

395 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

**1**answer

222 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

**1**answer

195 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

**0**answers

47 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

**0**answers

26 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

**1**answer

182 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

**2**answers

163 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

**1**answer

124 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

**0**answers

45 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

**2**answers

276 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 ...

**5**

votes

**2**answers

91 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

**2**answers

353 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

**2**answers

89 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

**1**answer

96 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

**1**answer

206 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 ...

**7**

votes

**1**answer

225 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?

**0**

votes

**0**answers

35 views

### Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not.
Which software would you suggest for rigid transformations?
Thank you

**-2**

votes

**1**answer

165 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 ...

**1**

vote

**0**answers

88 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

**1**answer

164 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

**1**answer

85 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

**1**answer

35 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
$$ ...

**1**

vote

**2**answers

412 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 ...

**15**

votes

**3**answers

562 views

### 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 ...

**3**

votes

**1**answer

111 views

### 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 ...

**9**

votes

**1**answer

316 views

### 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 ...

**3**

votes

**0**answers

127 views

### 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) ...

**1**

vote

**1**answer

73 views

### 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 ...

**13**

votes

**1**answer

228 views

### 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 ...

**2**

votes

**0**answers

30 views

### 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 ...

**4**

votes

**1**answer

117 views

### 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 ...

**5**

votes

**1**answer

273 views

### 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 $n$. ...

**1**

vote

**1**answer

110 views

### 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 ...

**4**

votes

**1**answer

132 views

### 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 ...

**2**

votes

**0**answers

51 views

### 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 ...

**34**

votes

**1**answer

2k views

### 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 ...

**4**

votes

**1**answer

338 views

### 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 ...

**6**

votes

**1**answer

125 views

### 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 ...

**62**

votes

**2**answers

2k views

### 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 ...

**5**

votes

**1**answer

79 views

### 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 ...

**5**

votes

**1**answer

289 views

### Subsets of all Diophantine's sets

I have asked this question on math.stackexchange already:
http://math.stackexchange.com/questions/627461/subsets-of-all-diophantines-sets
Function $\mathbb{N}^k \to \mathbb{N}^m$ is computable ...

**24**

votes

**10**answers

2k views

### Can We Decide Whether Small Computer Programs Halt?

The undecidability of the halting problem states that there is no general procedure for deciding whether an arbitrary sufficiently complex computer program will halt or not.
Are there some large $n$ ...

**4**

votes

**0**answers

243 views

### About “natural proof” of Razborov and Rudich

The famous "Natural Proof" paper ,http://www.cs.umd.edu/~gasarch/BLOGPAPERS/natural.pdf , of Razborov and Rudich gives a barrier for any proof that try to separate P and NP. It mainly shows that if ...

**3**

votes

**2**answers

200 views

### Place N points in a 3d cube in a way that maximizes the minimum of their pairwise distances

Place $N$ points in a 3d cube in a way that maximizes the minimum of their pairwise distances.
The problem can easily be solved for $N\lt5$, but how to proceed for larger $N$?

**5**

votes

**2**answers

506 views

### Why is there no product type in simply typed lambda-calculus?

Consider simply typed $\lambda$-calculus that has only the unit type as primitive. We would like to encode the product and the sum types. An encoding of the product type in the untyped ...

**6**

votes

**0**answers

730 views

### How many 2L-bit numbers are the product of two L-bit numbers?

If I multiply two integers $x, y $ in $[0,2^L)$, I get an integer in $[0,2^{2L})$. Clearly, this map from $[0,2^L) \times [0,2^L) \to [0,2^{2L})$ is not bijective.
I am interested in the size of ...

**15**

votes

**7**answers

1k views

### Two questions from combinatorics on words

Question 1. Assume that an infinite word $u\in\{0,1\}^{\mathbb Z}$ is not balanced. Is it true that there exists a finite 0-1 word $w$ such that $0w01w1$ or $1w10w0$ is a factor of $u$? Is it true ...

**5**

votes

**1**answer

122 views

### What prefix and factors determine a ultimately periodic word uniquely

Let $\xi$ be an ultimately periodic sequence, i.e. there exists finite sequences $p, q \in X^*$ such that $\xi = pq^{\omega}$. Does there exists a $n > 0$ such that the prefix of length $n$ and all ...

**0**

votes

**0**answers

74 views

### Proof of conjecture that permutation-free automata restrict the possible states visitable from a stringset sharing prefixes and infixes

An automaton $\mathcal A = (X, Q, \delta, q_0)$ is called permutation-free iff no word $w \in X^*$ induces a nontrivial permutation of a subset of the states of $\mathcal A$. More formally for any $R ...

**10**

votes

**2**answers

1k views

### How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...