From the link: The first attack, ConditionalExhaust, entails creating "two-faced" transactions that are computationally intensive only when executed by block creators that cannot include them in a block, while they are very simple & pay a low amount of fees in all other cases. We test ConditionalExhaust on a local testnet & show that with just 140 transactions costing at most $770, an attacker exhausts a victim's resources to the point where it cannot include any transaction in its blocks, thereby severely compromising the system's liveness.

The second attack, MemPurge, allows evicts honest transactions from a victim's mempool. Blockchain nodes save transactions in a size-limited database called the mempool. When the limit is reached, an existing transaction may be evicted in favor of a new & better paying one. MemPurge allows an attacker to send chains that are 65 transactions long, but which at the worst case require paying for just a single transaction, meaning that evicting transactions becomes considerably cheaper.