Parallel dynamics and computational complexity of the Bak–Sneppen model

The parallel computational complexity of the Bak–Sneppen evolution model is studied. It is shown that Bak–Sneppen histories can be generated by a massively parallel computer in a time that is polylogarithmic in the length of the history. In this parallel dynamics, histories are built up via a nested hierarchy of avalanches. Stated in another way, the main result is that the logical depth of producing a Bak–Sneppen history is exponentially less than the length of the history. This finding is surprising because the self-organized critical state of the Bak–Sneppen model has long range correlations in time and space that appear to imply that the dynamics is sequential and history dependent. The parallel dynamics for generating Bak–Sneppen histories is contrasted to standard Bak–Sneppen dynamics. Standard dynamics and an alternate method for generating histories, conditional dynamics, are both shown to be related to P-complete natural decision problems implying that they cannot be efficiently implemented in parallel.