# Tagged Questions

The tag has no wiki summary.

225 views

### Efficient representations of natural numbers via arithmetical expressions

A given natural number $n \in \mathbb{N}$ has many representations as expressions mixing other natural numbers and the operators and punctuation symbols $\{+,-,\times,/,\exp,(,)\}$, where '$\exp$' ...
473 views

### A generalization of the triangle counting problem for simple weighted graphs

One nice identity is $$tr(A^3)/6$$ which counts the number of triangles of a graph represented with adjacency matrix $A.$ It also implies that triangle counting can be performed in subcubic time. ...
62 views

### Can the isomorphism relation for countable models become harder when adding finitely many constants?

I am particularly interesting in the case where $T$ is o-minimal, but I would be interested in any theory $T$ (or even an $L_{\omega_1,\omega}$-sentence) which has this property. Context: view the ...
98 views

### $\mu$-recursive definitions for the complexity classes P, NP, etc

The standard complexity classes such as P, NP are usually defined using Turing Machines. In finite model theory those classes can be defined via the classical first-order/second-order logics. I am ...
89 views

### About infinite subset of halting probability and 1-random set

Let $\Omega$ be the halting probability (see (http://en.wikipedia.org/wiki/Chaitin's_constant) and R. Downey, and D. Hirschfeldt (2010), Algorithmic Randomness and Complexity for reference). If A is ...
231 views

### Is integer GCD in NC?

Wikipedia, in the page http://en.wikipedia.org/wiki/Greatest_common_divisor#Complexity mentions integer GCD is in NC by citing http://www.cs.cornell.edu/courses/CS6820/2012sp/Handouts/Sedjelmaci07.pdf ...
This is an agglomeration of several questions, linked by a single observation: SAT is equivalent to determining the existence of roots for a system of polynomial equations over $\mathbb{F}_2$ (note ...