7 papers
The Nesting Bird Box Problem is ER-complete: Sharp Hardness Results for the Hidden Set Problem
Lucas Meijer, Till Miltzow, Johanna Ockenfels +1
In the (Nesting) Bird Box Problem we are given a polygonal domain P and a number k and we want to know if there is a set B of k points inside P such that no two points in B can see…
Beyond Bits: An Introduction to Computation over the Reals
Tillmann Miltzow
We introduce a lightweight and accessible approach to computation over the real numbers, with the aim of clarifying both the underlying concepts and their relevance in modern resea…
Sometimes Two Irrational Guards are Needed
Lucas Meijer, Tillmann Miltzow
In the art gallery problem, we are given a closed polygon , with rational coordinates and an integer . We are asked whether it is possible to find a set (of guards) of si…
Recognition of Unit Segment and Polyline Graphs is -Complete
Michael Hoffmann, Tillmann Miltzow, Simon Weber +1
Given a set of objects in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corres…
Devil's Games and : Continuous Games complete for the First-Order Theory of the Reals
Lucas Meijer, Arnaud de Mesmay, Tillmann Miltzow +2
We introduce the complexity class Quantified Reals (). Let FOTR be the set of true sentences in the first-order theory of the reals. A language is in $\text…
On Equivalent Characterizations of NP in Abstract Models of Computation
Jeremy C. Kirn, Lucas Meijer, Tillmann Miltzow +1
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure , and we show that under weak conditions on $\…