6
votes
1answer
32 views

Integer programming feasibility is NP-what

What is the complexity class of the general problem of integer programming feasibility? The sources I've looked at are, in my opinion, very confusing. Some say NP-hard, some say NP-complete. Some ...
0
votes
0answers
23 views

Basic questions about descriptive complexity

I'm trying to learn descriptive complexity, and I'm having trouble on a basic level wrapping my head around what it means for a logical formula to define a computational language. I've tried and ...
0
votes
0answers
11 views

Proof of theorem about connection between nondeterministic and deterministic Turing machines complexity classes

I need source for proof of this theorem: Every $T(n)$ time nondeterministic Turing machine has an equivalent $2^{O(T(n))}$ deterministic Turing machine. I have book by Michel Sipser, ...
0
votes
0answers
13 views

What are the current lower bounds for $NTIME$ vs $DTIME$?

Trivially, we have $DTIME(f(n)) \subset NTIME(f(n))$. Is it known whether or not this inclusion is strict? Do we know if $DTIME(f^c(n)) \subset NTIME(f(n))$ for any $c$? Is there any $c$ for which ...
0
votes
3answers
40 views

Reference for problems without efficient algorithm (in polynomial time)

I'm writing paper and need your help in finding some famous (or not so famous) problems without efficient algorithm, but from logic or computer science. So far, I have: -Boolean satisfiability ...
1
vote
1answer
91 views

Complexity of the algorithms for Singular Value Decomposition

As said in the title, I would like to find out something on the numerical algorithms for computing the SVD decomposition of a rectangular matrix, with particular regard to their the computational ...
1
vote
0answers
43 views

Why is positional number system natural?

In the theory of computation, one mainly deals with maps $\Sigma^*\rightarrow\Sigma^*$. To discuss computation on other sets $X$ than $\Sigma^*$, one fixes a representation ...
7
votes
1answer
410 views

efficient summation of $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n}\sum_{l=1}^{n}A_{ij}A_{ik}A_{il}A_{jk}A_{jl}A_{kl}$

I want to find an efficient algorithm for calculating a sum of products with entangled indices. For example, $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n} A_{ij}A_{jk}A_{ki}$, where $A_{ij}$ is the a ...
3
votes
1answer
132 views

Books on computational complexity

Can anyone recommend a good book on the subjects of computability and computational complexity? What are the de facto standard texts (say, for graduate students) in this area? I've heard a thing or ...
4
votes
2answers
238 views

Is there a function that only generates primes?

The title sums it up: does there exist a "nice" injective function $f(n)$ such that $f(n)\in\mathbb P$ for all $n\in\mathbb N$? I'm having difficulty specifying exactly what I want "nice" to mean, ...
1
vote
2answers
700 views

Is there a winning strategy for Scrabble?

I am sure many of us are addicted to the popular Facebook app: Words with Friends, which is basically an online version of Scrabble. In Playing Games with Algorithms:Algorithmic Combinatorial Game ...
4
votes
0answers
167 views

Proving NP-completeness (hardness) exercises

I am looking for a list of exercises that can be done to practice polynomial time reductions to prove NP-hardness of problems. I know there are hundreds (thousands?) of problems proven to be NP-hard. ...
5
votes
2answers
327 views

Is there a log-space algorithm for divisibility?

Is there an algorithm to test divisibility in space $O(\log n)$, or even in space $O(\log(n)^k)$ for some $k$? Given a pair of integers $(a, b)$, the algorithm should return TRUE if $b$ is divisible ...
2
votes
1answer
59 views

Specific solvable cases of TSP

Did a quick search on polynomial time solvable TSP and found some references such as this one for special cases for the bottleneck TSP. Was wondering if anyone was aware of any references that catalog ...