**6**

votes

**1**answer

129 views

### Is it possible to make an algorithm that could predict the likelihood that a program will halt? [on hold]

Today I began to read about computability theory. I do not even have an elementary understanding of the topic but it certainly got me thinking. I know there is there is no 'one-for-all' algorithm that ...

**-2**

votes

**0**answers

34 views

### how to solve recurrence using substitution method T (n) = T (n-1) + c [closed]

how to solve recurrence using substitution method T (n) = T (n-1) + c
how to solve this recurrence T (n) = T (n-1) + c using substitution method for Advanced Algorithm Analysis and Design purpose

**-5**

votes

**0**answers

34 views

### Hamiltonian systems plus epsilon [closed]

EDIT: A $2n$-dimensional hamiltonian system is completely integrable if it has $n$ linearly independent (over $\mathbb R$) conserved observables ($C^\infty$ functions on phase space, among which is ...

**14**

votes

**2**answers

404 views

### Can a stochastic Turing machine output a consistent extension of PA with positive probability?

Suppose that we interpret the output tape of a Turing machine as an assignment of true or false to all sentences of PA, taking the $n$th output bit as the truth value of the sentence with Goedel ...

**33**

votes

**2**answers

2k views

### What are the implications of the new quasi-polynomial time solution for the Graph Isomorphism problem?

This week, news came out that Laszlo Babai has found a quasi-polynomial time algorithm to solve the Graph Isomorphism problem (that is: $O(\exp(polylog(n)))$). He is giving a series of talks this ...

**1**

vote

**0**answers

31 views

### Efficient SVD of a matrix without some of the columns

I have a matrix $A \in \mathbb{R}^{p \times q}$ of rank $r$ and its SVD decomposition, i.e,
$$
A = U S V^\top,
$$
where $U \in \mathbb{R}^{p \times r}$ and $V \in \mathbb{R}^{q \times r}$ are ...

**4**

votes

**1**answer

69 views

### What class of probability distributions do probabilistic turing machines induce? [closed]

What class of probability distributions is induced by the class of probabilistic turing machines? Is there a precise characterization?

**1**

vote

**0**answers

53 views

### Monoidal cats and string diagrams for a semantics of object oriented programming languages

It seems to me that in a statically typed, object oriented language, there is a striking similarity to wiring diagrams. Wires (objects) of type $X$ go into functions (boxes) of input type $X$. Is ...

**13**

votes

**0**answers

125 views

### Complexity classes for BSS machines

Given a first-order structure $\mathcal{S}$, a Blum-Shub-Smale machine on $\mathcal{S}$ is essentially a Turing machine where
Cells on the tape can hold arbitrary elements of $\mathcal{S}$.
The ...

**3**

votes

**1**answer

110 views

### Equivalence between Diffie Hellman and Discrete Log

For which non-trivial groups, do we know that the Diffie Hellman problem and the Discrete Log are equivalent?
Is there any group for which we suspect them to be different?
Could there be a finite ...

**1**

vote

**0**answers

62 views

### Optimal reduction using token-passing nets

I am looking for implementation of optimal reduction for λ-calculus based on interaction nets (McCarthy's amb allowed) in the spirit of "Token-Passing Nets: Call-by-Need for Free" by François-Régis ...

**7**

votes

**1**answer

130 views

### Shortest vector problem over polynomials

In shortest vector problem, given a lattice in $\Bbb Z^n$, we seek the shortest non-zero vector in the lattice. This problem is computationally difficult.
Is there a polynomial analog of this problem ...

**5**

votes

**0**answers

105 views

### Constructive Mathematics and Termination [closed]

In the book "The Universal Turing Machine A Half-Century Survey" there is a paper called "The Confluence of Ideas in 1936" by Robin Gandy. In section 4.2, Gandy writes:
"If one accepts, on whatever ...

**7**

votes

**1**answer

164 views

### “Separated” version of Sauer's lemma on VC classes

Sauer's lemma, a well-known result in computational complexity theory, learning theory, and combinatorics, states the following:
Let $\Phi$ be a collection of subsets of a set $U$, and assume that ...

**1**

vote

**1**answer

50 views

### floating point representation via the perspective of TTE/computable analysis

Floating point numbers are not compatible with the usual theory of type 2 theory of effectivity (TTE), and not even the real-RAM model; there are functions that are computable in one model but not ...

**18**

votes

**0**answers

531 views

### Reference request: Parallel processor theorem of William Thurston

Sometime in the 1980's or 1990's, Bill Thurston proved a theorem regarding the existence of a universal parallel processing machine, using a certain class for such machines having finite deterministic ...

**-1**

votes

**1**answer

232 views

### Are limits decidable? Should definitions be decidable? [closed]

This question is about the Turing computability of the $\epsilon-N$ definition of a limit of an infinite sequence $S$. First, a proposition:
There cannot exist a Turing Machine $M$ which, given a ...

**3**

votes

**0**answers

104 views

### Oracle queries asked in parallel

Definition: Assume that $\phi(q)$ is of the form $\exists y \leq 2^{p(n)} \varphi(q,y)$, where $p$ is a polynomial and $n = |q|$ (i.e. $n$ is the length of the binary representation of $q$). Then a ...

**3**

votes

**0**answers

228 views

### Possible $\mathsf{NP}$ complete problem from number theory

A candidate $\mathsf{NP}$ complete variant of factoring was posted in http://cstheory.stackexchange.com/questions/4769/an-np-complete-variant-of-factoring, where decision problem ...

**5**

votes

**2**answers

179 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 ...

**1**

vote

**1**answer

50 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 ...

**1**

vote

**0**answers

35 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

**0**answers

46 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 ...

**1**

vote

**0**answers

22 views

### Open volumetric time series data set

Does anyone know where I can find a good open volumetric time series data set?
I had a look at some of Stanford's open data sets (https://graphics.stanford.edu/data/voldata/ )
But these do not seem ...

**22**

votes

**3**answers

846 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 ...

**7**

votes

**0**answers

150 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 ...

**11**

votes

**3**answers

700 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 ...

**6**

votes

**0**answers

219 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 ...

**2**

votes

**1**answer

281 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 ...

**3**

votes

**0**answers

142 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

**1**answer

140 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."
...

**5**

votes

**1**answer

406 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 ...

**6**

votes

**1**answer

143 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

**1**answer

543 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

**0**answers

97 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

**0**answers

73 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

**0**answers

322 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

**1**answer

110 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

**1**answer

88 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

**0**answers

188 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

**1**answer

681 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

**0**answers

71 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 ...

**5**

votes

**2**answers

878 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

**2**answers

335 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

**1**answer

185 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

**1**answer

163 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

**0**answers

83 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

**2**answers

441 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

238 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

212 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 ...