1
vote
1answer
28 views

Computational complexity of expanding a MacLaurin/Taylor Series

What methods exist to computationally determine the first $k$ coefficients of a function (possibly polynomial or rational polynomial function)? How do Mathematica/MatLab/Maple/etc. solve this ...
1
vote
0answers
333 views

Solving large, sparse system of linear equations

I have a system of linear equations as follows: $$(A+I)x=B$$ where $I$ is the $n\times n$ identity matrix, $A$ is a $n\times n$ matrix such that the first and last rows are blank, and, for every ...
2
votes
0answers
80 views

Solving a particular system of Diophantine equations in $n$ variables (Frobenius equations)

I have a particular system of linear Diophantine equations in $n$ variables for which I need to find all nonnegative integer solutions. Specifically, they are Frobenius equations, meaning the ...
0
votes
0answers
34 views

Polytime programming

Given a linear system of the form: $$x_r = a$$ $$x_j = b$$ $$c_1x_1 + c_2x_2 ... c_nx_n = n$$ $$x_1 + x_2 + x_3 ... x_n = k $$ $$0 \leq a,b,x_1, x_2, x_3 ... x_n \leq 1$$ $$k \geq 0$$ How quickly ...
4
votes
4answers
310 views

Computing partition numbers

Today a friend and myself came up with the question of computing partitions of numbers, i.e.: given a number $n$, what is the number $p(n)$ of was of different ways writing $n$ as a sum of non-zero ...
2
votes
1answer
89 views

What does noncomputable really mean?

I believe I understand the definition of a noncomputable problem from an introductory computer science class, but I don't understand what it really means. One of my hypothesis was that a ...
6
votes
1answer
362 views

How to find an expression whose value is 190

Given a set of numbers (in this case): 3, 7, 7, 100, 50 Either: prove it is impossible to form the number k = 190 using ( ) + - * / operators between sub set of the these numbers ex: 1000 = ((3 + ...
2
votes
2answers
97 views

Number of ways to move 1 or more elements from one list to the previous list until one list remains

Given N elements, divided into at most N groups, which are then labeled 1 thru N, move all of the elements into the group labeled 1. By moving 1 to all of the elements, in group i to i-1. This means ...
2
votes
1answer
120 views

Oracle turing machine

I am learning computational complexity and this is a question of my assignment that I have issues trying to solve/understand. An oracle Turing Machine M with oracle A is a Turing Machine with an ...
2
votes
1answer
206 views

Complement of NP-Complete

If a language L is NP-complete, with respect to polynomial time reducibility, does L ≤ co-L in polynomial time?
0
votes
0answers
182 views

How a direct method can be compared with an iterative method?

How a direct method can be compared with an iterative method? I have an iterative method to compute Moore- penrose generalized inverse. There are some direct methods available to compute Moore-Penrose ...
1
vote
1answer
71 views

Finding the computational complexity of an algorithm

Algorithm: for (int i = 0; i < 2*n; i += 2) for (int j = n; j >i; j--) foo(); I want to find the number of times foo() is called. ...
0
votes
1answer
69 views

$T(n) = n^{O(1)}$ iff exists $k > 0$ such that $T(n) = O(n^k)$

I must use O notation to show that: $T(n) = n^{O(1)}$ iff exists $k > 0$ such that $T(n) = O(n^k)$ But, I don't understand what mean: $n^{O(1)}$
1
vote
1answer
219 views

Structure and Formula encoding for Turing Machine

During my study of Finite Model Theory I found that usually purely relational structure say $\mathcal{M} = \langle A, R_1,\ldots,R_k \rangle$ are encoded as ...