Lattice Gas Prediction is P-complete

Abstract

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^α) for α< 1/2, unless the class P is equal to the class NC or SP respectively.