The saturation strategy for symbolic state-space generation is very effective for globally-asynchronous locally-synchronous discrete-state systems. Its inherently sequential nature, however, makes it difficult to parallelize on a NOW. An initial attempt that utilizes idle workstations to recognize event firing patterns and then speculatively compute firings conforming to these patterns is at times effective but can introduce large memory overheads. We suggest an implicit method to encode the firing history of decision diagram nodes, where patterns can be shared by nodes. By preserving the actual firing history efficiently and effectively, the speculation is more informed. Experiments show that our implicit encoding method not only reduces the memory requirements but also enables dynamic speculation schemes that further improve runtime.