2 research outputs found
Lattice Gas Prediction is P-complete
We show that predicting the HPP or FHP III lattice gas for finite time is
equivalent to calculating the output of an arbitrary Boolean circuit, and is
therefore P-complete: that is, it is just as hard as any other problem solvable
by a serial computer in polynomial time.
It is widely believed in computer science that there are inherently
sequential problems, for which parallel processing gives no significant
speedup. Unless this is false, it is impossible even with highly parallel
processing to predict lattice gases much faster than by explicit simulation.
More precisely, we cannot predict t time-steps of a lattice gas in parallel
computation time O(log^k t) for any k, or O(t^\alpha) for \alpha < 1/2, unless
the class P is equal to the class NC or SP respectively.Comment: 10 pages with figure
Two-dimensional FHP lattice gases are computation universal.β Complex Systems 7
Abstract. We show that the FHP lattice gases are computation universal, implying that general questions about their behavior are undecidable. The proof embeds a universal one-dimensional cellular automat on in the two-dimensional FHP lattice gas. This provides evidence that general questions about fluid behavior are undecidable. 1