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0
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1answer
441 views

Transition Graph per alphabet?

How do you determine how many different Transition Graphs are over a particular alphabet? For example How many TG's are over the alphabet {x, y}. I am taking a class with a similar question from ...
2
votes
1answer
1k views

How many cpus needed to check a 100 million digit prime number efficiently? [closed]

If I had access to potentially unlimited CPUs and wanted to quickly check 100 million digit numbers for primality using a map-reduce architecture, how many CPUs would be necessary? Each of the mapped ...
1
vote
3answers
331 views

Operator probability in a RPN string

Consider the set $S_n$ of all strings of length $n$ ($n$ integer, $n \geq 3$) representing an expression in RPN ( http://en.wikipedia.org/wiki/Reverse_Polish_notation. ) Assumptions (to simplify): ...
1
vote
2answers
443 views

Hash functions and inner product

Hi all, As a part of a research I'm working on (involving derandomization of linear threshold functions), I'm trying to understand the following problem: Is there a small (polynomial rather than ...
1
vote
1answer
393 views

Decomposing a sphere (or defomed sphere) into a vertex-transitive graph with fixed-length curved edges

Please see the original problem specification (which Joseph O'Rourke was responding to in his answer) below. Motivation - I'm interested in a particular case of the problem where one wants to ...
1
vote
0answers
201 views

Geometric/Analytic techniques for constructive and asymptotic bounds in the Lee metric

Slight extension of cross posting from http://cstheory.stackexchange.com/questions/7408/lee-metric-gilbert-varshamov-and-hamming-bounds-for-larger-relative-distance-rang (closed there) The following ...
1
vote
1answer
257 views

Constructing a graph that approximates a sphere using rotationally symmetric building blocks with equal numbers of edges

I'd like to construct a graph that approximates a sphere in 3-space, but I'm placed under the following constraints: (1) - I am only allowed to use a construction block, $v_i$, consisting of a single ...
5
votes
6answers
2k views

Fast evaluation of polynomials

Hello everybody ! I was reading a book on geometry which taught me that one could compute the volume of a simplex through the determinant of a matrix, and I thought (I'm becoming a worse computer ...
1
vote
1answer
125 views

Inferring geometric properties of a polytope from intersection volumes of spheres at unknown coordinates on its surface

Let's say we have some polytope $P$ in 3-space (which is not necessarily convex) as well as some number of points on its surface, $(g_1, ..., g_N)$. We are provided no information about the ...
1
vote
0answers
335 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
1answer
411 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 ...
4
votes
1answer
315 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 ...
6
votes
1answer
497 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
1answer
257 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
1answer
412 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
2answers
226 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
1answer
585 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
3answers
2k 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
2answers
435 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
1answer
151 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
5answers
565 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 ...
9
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0answers
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
3answers
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
0answers
80 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
0answers
212 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
2answers
470 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
1answer
177 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
1answer
528 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
2answers
550 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
2answers
310 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 ...
1
vote
0answers
725 views

Lambert's Cosine Law - Simple algebraic rearrangement problem [closed]

Let $I(x,y)$ be the intensity at position $(x,y)$, $\rho(x,y)$ be the albedo at this point (a constant), $n=(p,q,1)$ be the surface gradient vector and $s_{0},s_{1},s_{2}$ all be vectors from the ...
8
votes
1answer
1k 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
1answer
338 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
2answers
321 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 ...
5
votes
2answers
452 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
3answers
514 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 ...
1
vote
0answers
336 views

Catmull-Clark Subdivision and weights

I've been toying with a Catmull-Clark subdivision algorithm; I also compared my results to results I found online (e.g. images.google.com). The weights used to relocate the old vertices of the mesh ...
4
votes
1answer
239 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
1answer
210 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
2answers
257 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
2answers
661 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
2answers
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
5answers
408 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
1answer
248 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
1answer
413 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 ...
0
votes
0answers
370 views

Applications of the property of Kendall-Mann numbers

I am looking for an application of the Kendall-Mann sequence (KM) which uses the property $M(n+1)/M(n) = n - 1/2 + O(1/n)$ ($n \to \infty$) in science ( computer science ( sorting), physics, biology ...
26
votes
17answers
6k 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
2answers
703 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 ...
6
votes
1answer
365 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
2answers
559 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 $N$ ...