All Questions

A classical theorem in Integer Programming by Lenstra says that any integer system $$A x \le b$$ can be solved in polynomial time, where $A \in \mathbb{Z}^{m \times n}, x \in \mathbb{Z}^n, b \in \...

Is there a way to show within an integer program with constant number of variables and constraints of length $poly(\log B)$ (say length $\leq10^{1000000}\log B$), it is not possible for a variable to ...

We do not know if $P=NP$ or not or if there is a superfast integer mutiplication algorithm. But I do not think either assumption is necessary to answer this question. Is there a way to show within an ...

Definable subsets of $\mathbb N$ in the language of Presburger arithmetic are exactly the eventually periodic sets and quantifier free part corresponds to Integer Programming with linear inequalities. ...