This paper explores the impact of geometry on computability =
and complexity in
Winfree's model of nanoscale self-assembly. We work in the =
two-dimensional
tile assembly model, i.e., in the discrete Euclidean plane Z x Z. Our =
first
main theorem says that there is a roughly quadratic function f ... more >>>

An aperiodic tile set was first constructed by R.Berger while
proving the undecidability of the domino problem. It turned out
that aperiodic tile sets appear in many topics ranging from
logic (the Entscheidungsproblem) to physics (quasicrystals)

We present a new construction of an aperiodic tile set. The
flexibility of this ... more >>>

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results.

1. NP ... more >>>