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We present a classification that groups lookback into fourtypes: direct strong lookback, universal strong lookback, directweak lookback, and universal weak lookback. They aredefined in terms of absolute and dynamic impact times. Wediscuss relationships between lookback types by consideringwhen rollbacks and/or anti-messages are avoided. Fromdifferent types of lookback, we also derive three optimizationtechniques for optimistic simulation and point out theiradvantages over lazy cancellation. Finally, we show that allfour types of lookback exist in the PCS network simulationand can be exploited by either lookback-based or optimisticprotocols.