# The Banner Image ...

... shows part of the blackboard after a research session together with Stefan Schwoon in summer 2001, which resulted in the following journal publication:

[1] |
M. Holzer and St. Schwoon. Assembling
Molecules in Atomix is Hard. Theoretical
Computer Science, 313(3):447-462, February 2004.
DOI It is shown that assembling molecules in the Atomix game can be used to simulate finite automata. In particular, an instance of Atomix is constructed that has a solution if and only if the non-emptiness intersection problem for finite automata is solvable. This shows that the game under consideration is PSPACE-complete, improving a recent result of Hüffner et al. (Lecture Notes in Computer Science, Vol. 2174, Springer, Vienna, Austria, 2001, pp. 229--243). Moreover, the given reduction shows that there are Atomix games which have exponentially long optimal solutions. We also give an easy construction of Atomix game levels whose optimal solutions meet the worst case. |

How to assemble a water molecule is shown in the following animated gif-movie,

which was created with MetaPost and gifmerge.