**1**

vote

**0**answers

343 views

### NP-complete variants of NPI problems

Motivated by these posts, An NP-complete variant of factoring and Relationship between symmetry and computational intractability, It seems to be worthwhile to investigate the different factors that ...

**8**

votes

**1**answer

477 views

### Magma “actions” (or alternatively, “What is the Yoneda lemma for magmas?”)

Arguably the most import thing about groups, semigroups and more generally categories, is that they can act on sets (or even collections of sets in the case of a category). This is the basis for all ...

**5**

votes

**1**answer

358 views

### Growth zeta-functions of regular languages

Dear All,
my following question may be known and ought to be known, so in case it is folklore please could you give me the references.
To start, it is obvious that growth of rational languages are ...

**7**

votes

**1**answer

594 views

### The hardness of computing inverse

Say we have a one-to-one (total) function $f:\mathbb{N}\to\mathbb{N}$ and a Turing-machine $T_f$ that computes it. Suppose further that $T_f$ runs in polynomial time wrt. length of the input.
Are ...

**2**

votes

**1**answer

297 views

### Given a PDA M such that L(M) is in DCFL construct a DPDA N such that L(N) = L(M)

Is it possible to construct an algorithm which takes as input a pushdown automaton $M$ along with the information that the language accepted by this automaton $L(M)$ is a deterministic context-free ...

**2**

votes

**1**answer

439 views

### Lipschitz constant of Laplace-Beltrami Operator

I already asked this question at stackexchange with no response - so I'll try here.
I'm reading a paper on discrete differential geometry:
Meyer et.al.
They define the Laplace-Beltrami operator at ...

**2**

votes

**2**answers

229 views

### Correcting bias in samples selected by a prediction

Here is the scenario:
I'm trying to find as many golden tickets as I can, so that I can sell them to kids that want to go on a tour of Wonka's chocolate factory.
Fortunately, I have a machine that ...

**2**

votes

**1**answer

764 views

### Official name and complexity of k-way balanced set partitioning? What is the best heuristic?

As a lot of people know, graph partitioning is NP-Complete. In graph partitioning, you try to create k balanced (within some pre-specified epsilon) disjoint subsets of (possibly weighted) vertices ...

**2**

votes

**3**answers

3k views

### Worst known algorithm in terms of Big-O (more precisely Big-theta)?

Hello,
I have been trying to find the worst algorithm in terms of it's Big-O function. By worst I mean n! is worse than n^2, n^n is worse than n!, etc. Essentially the worst algorithm would be the ...

**3**

votes

**2**answers

512 views

### Partition a square into sub-rectangles with restrictions

Is there an algorithm to generate all partitions of given square by using $n$ vertical and $n$ horizontal lines into sub-rectangles under the following restrictions:
1- No vertical line crosses any ...

**0**

votes

**1**answer

163 views

### the maximal length of a special dicksonian sequence

First, we define a sequence $t_{1},t_{2},\cdots,t_{k}$ of n-tuples dicksonian, if $\forall 1\leq i < j\leq k,$ there does not exist a non-negative n-tuple t such that
$t_{i}+t=t_{j}.$ For example, ...

**3**

votes

**5**answers

589 views

### Is the following two-dimensional graph likely to be globally rigid?

Consider the two-dimensional non-planar graph $G$, with known topology and edge lengths $(r_1, r_2, ... r_N) \in R$, but unknown vertex coordinates. We further specify that:
All vertices within a ...

**8**

votes

**0**answers

1k views

### Question on randomness extractors

Person A has a source $W$ with min-entropy($W$) = $k$. He also has an extra piece of information about the random source, denoted with $y$, such that min-entropy($W|y$) = $k/3$.
The adversary doesn't ...

**26**

votes

**3**answers

2k views

### “Simpler” statements equivalent to Con(PA) or Con(ZFC)?

Given any reasonable formal system F (e.g., Peano Arithmetic or ZFC), we all know that one can construct a Turing machine that runs forever iff F is consistent, by enumerating the theorems of F and ...

**0**

votes

**0**answers

99 views

### Does there exist an algorithm for computing reachability in dynamic directed forests with fast update?

I'm interested in an algorithm which is able to compute reachability between any two nodes in polylog update (add or remove a valid edge) and query. I know that such an algorithm does exist for all ...

**2**

votes

**0**answers

243 views

### what is the largest gap between rank and approximate rank

$\epsilon$-approximation rank of a matrix $M$ is the minimum rank of a real matrix $A$ which differs from $M$ at most $\epsilon$ in each entry. Associating any function $f:X\times Y\rightarrow${1,-1} ...

**1**

vote

**2**answers

634 views

### best deterministic complexity for factoring polynomials over finite field

I would like to know currently what's the best deterministic complexity for factoring polynomials over finite field (without the assumption of GRH)? I have searched on google, there are many source, ...

**2**

votes

**1**answer

188 views

### Parsing of Stochastic Contex-Free Grammars (SCFGs)

I am interested in parsing of general SCFGs.
I am aware of the Earley parser for the general CFGs. The only general algorithm for parsing SCFGs that I am aware of is the Earley-Stolcke parser : ...

**1**

vote

**1**answer

559 views

### final step(s) for a proof that a function is not primitive recursive

My function is $f:\mathbb{N} \rightarrow \mathbb{N},\ f(n)=2\uparrow ^n 3$ , the Ackermann(-Péter) function, with the second argument fixed to 3 (and "$\uparrow$" the Knuth up-arrow), which I believe ...

**15**

votes

**2**answers

636 views

### Status of an open problem about semilinear sets

In his book "The Mathematical Theory of Context-Free Languages" (1966), Ginsburg mentioned the following open problem:
Find a decision procedure for determining if an arbitrary semilinear set
is ...

**4**

votes

**2**answers

320 views

### Approximate search space on a 5x5x5 cube with 3 different possible classes?

Hey all,
I read the meta, and I realize this question might be pretty elementary for this site, but I'm having trouble computing this, and I know it won't take too much insight for someone to give me ...

**9**

votes

**1**answer

2k views

### All-pairs shortest paths in trees?

This is a reference request, since I'm sure what follows isn't new, but I can't seem to find it.
Suppose that we have a finite tree $T$ with non-negative weights on the edges. Naively, computing the ...

**4**

votes

**1**answer

363 views

### Injections to binary sequences that preserve order

Suppose we have a countable set S with a total order. Can we give an injection from S to the set of finite binary sequences that end in all zeros that preserves the ordering? The order on binary ...

**3**

votes

**2**answers

341 views

### Finding the solution to b = Ax that minimizes the Hamming weight (everything over the field F_2).

Is there an efficient algorithm for finding the solution $x$ of
$b = Ax$
that minimizes the Hamming weight of $x$, where
$A$ is a nxm-matrix over the field $\mathbb{F}_2$ ("integer matrix modulo ...

**6**

votes

**2**answers

518 views

### A Query regarding the Halting Problem (Omega): Halting Probability for Given Input Size

I was studying the Halting Problem in context of the Probability and had a few doubts regarding it. Hope someone could help me out.
I am aware of the probability of a Random program halting on a ...

**5**

votes

**3**answers

533 views

### Appropiate models of numerical computation

Hello,
in contrast to the more discrete part of computational mathematics (cryptography, combinatorial computation), numerical mathematics seems to ignore typical questions of theoretical computer ...

**4**

votes

**1**answer

248 views

### Turing Machine which generates order on the set of its states

This question is related to this one Do Turing Machines generates any nontrivial lattice on the set o symbols or states?
The Turing machine (TM) is an abstract model for effective implementation of ...

**1**

vote

**1**answer

215 views

### Do Turing Machines generates any nontrivial lattice on the set o symbols or states?

Second question, probably better: Turing Machine which generates order on the set of its states
I would like to ask ( if it is not terribly obviously wrong):
Do Turing Machine generates ...

**1**

vote

**2**answers

301 views

### Positive & Negative Arity

Hi,
You can talk about the arity of a function or an operation - something like addition could have an arity of 2, and negation usually has an arity of 1.
A paper I am reading is talking about ...

**2**

votes

**2**answers

740 views

### viewing the second fundamental form as a tensor

Dear all,
Thank you for your time reading this post. I am a student in computer science so this viewpoint of the second fundamental form may be interesting to you.
I would like to understand the ...

**3**

votes

**2**answers

1k views

### finding numbers at k hamming distance

Guys,
I have N < 2^n randomly generated n-bit numbers stored in a file the lookup for which is expensive. Given a number Y, I have to search for a number in the file that is at most k hamming ...

**8**

votes

**5**answers

432 views

### Syntactically capturing complexity classes

Primitive recursive functions are syntactically constructible in the sense that from a set of "axioms" we can build every function in the set $PR$. This basicly means that we can build a machine that ...

**1**

vote

**1**answer

260 views

### Can a polynomial size CFG describe the finite language \{$w \pi(w)$ : $\pi(w)$ is fixed string permutation, $|w|=n$ is fixed\} over alphabet \{0,1\}?

Can a polynomial size Context free grammar describe the finite language {$w \pi(w)$ : $\pi(w)$ is fixed string permutation, $|w|=n$ is fixed} over alphabet of {0,1}?
One case this is possible is when ...

**4**

votes

**1**answer

552 views

### What fails when using call/cc as realizer of the Peirce formula

Define the axiom constants $p_{A,B}^{((A\rightarrow B)\rightarrow A)\rightarrow A}$ as realizers of the Peirce formula, and $f_A^{\bot\rightarrow A}$ as realizers of the Ex Falso Quodlibet. Then ...

**28**

votes

**17**answers

7k views

### Computer Science for Mathematicians

This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet.
I've seen computer scienctists post questions looking to learn things ...

**1**

vote

**2**answers

778 views

### Verifying a sequence that converges to pi [closed]

A computer program ouputs the digits of $\pi$ by evaluating the recurrence relation
$a_{n+1} = a_n + sin \ a_n$
with $a_0 = \frac{6}{5}$
Does the sequence actually converge or is this just ...

**5**

votes

**1**answer

434 views

### What is the pathwidth of the 3D-grid (mesh or lattice) with sidelength k?

This question is now also on http://cstheory.stackexchange.com/questions/4081/what-is-the-pathwidth-of-the-3d-grid-mesh-or-lattice-with-sidelength-k, where a discussion started, and one reference ...

**4**

votes

**2**answers

666 views

### Coloring edges on a graph s.t. the set of edges for any two vertices have no more than 'k' colors in common

Please imagine the case where one has a planar graph, $G$, with a set of $|V|$ vertices, $(v_1, ..., v_{|V|}) \in V$, and $|E|$ edges, $(e_1, ..., e_{|E|}) \in E$. Now, provided a total of $N$ ...

**8**

votes

**3**answers

2k views

### n-dimensional voronoi diagram

Hi, I need to compute the voronoi diagram of a set of points in $R^n$.
I'm quite unschooled on the topic, could someone point me to the right references so that I can
a) understand the theory behind ...

**6**

votes

**1**answer

369 views

### Are innermost reductions perpetual in untyped $\lambda$-calculus?

Background
In the untyped lambda calculus, a term may contain many redexes, and
different choices about which one to reduce may produce wildly
different results (e.g. $(\lambda x.y)((\lambda ...

**2**

votes

**3**answers

320 views

### Can we uniquely define a graph to have the topology of a polytope via proper edge length selection?

I'll ask you to consider a situation wherein one has a series of edges for a graph, $(e_1, e_2, ..., e_N) \in E$, each with a specifiable length $(l_1, l_2, ..., l_N) \in L$, and the goal is to insure ...

**0**

votes

**1**answer

1k views

### How are taps proven to work for LFSRs?

Obviously, you can exhaustively check that it lands on every state except the zero state, but for large linear feedback shift registers (LFSR), this quickly becomes infeasible.
Wikipedia states the ...

**15**

votes

**7**answers

2k views

### Between mu- and primitive recursion

It is well known that primitive recursion is not powerful enough
to express all functions, Ackermann function being probably the best
known example.
Now, in the logic courses (that I have had look ...

**5**

votes

**1**answer

336 views

### Drawing graphs on circles

Please consider the following problem:
Given: a simple graph (without self-loops and without multiple edges) $G$ on $n$ vertices.
Task: place equidistantly the vertices of $G$ on a circle of unit ...

**6**

votes

**1**answer

4k views

### Meaning of \Subset notation

The symbol $\Subset$ (occurring in places where $\subseteq$ could occur syntactically) comes up frequently in a paper I'm reading. The paper lives at the intersection of a few areas of math, and I ...

**29**

votes

**1**answer

3k views

### An edge partitioning problem on cubic graphs

Hello everyone,
I already asked this question on the TCS Stack Exchange, but it has not been resolved yet. Maybe readers of this forum will have other ideas or information, although I suspect that ...

**6**

votes

**1**answer

463 views

### post correspondence problem variant

Is there an algorithm which takes as input two lists of words $v_1,...,v_n$ and $w_1,...,w_n$ over an alphabet $X$ and decides if there is an infinite sequence $(k_i)$ where $1 \leq k_i \leq n$ for ...

**4**

votes

**3**answers

1k views

### Optimal packing of spheres tangent to a central sphere

Please consider a central, ordinary 2-sphere $S_1$, of some radius $r_1$, and a second ordinary sphere, $S_2$, of radius $r_2$, where $r_2 \leq r_1$.
My question concerns optimal values for the ...

**0**

votes

**3**answers

298 views

### boolean functions and averaging / counting

Hey guys,
I have a slightly imprecise question. I would like say something about a whole set of binary strings evaluated by a binary function by just looking at some type of average. The easiest ...

**1**

vote

**2**answers

907 views

### What is the right citation for the power iteration method to find eigenvalues?

What is the right citation for the power iteration method to find eigenvalues, if I want to cite the method in a paper? I've seen some Google PageRank references in this context. But Brin and Page ...