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Traditional public blockchain systems typically had very limited transaction throughput because of the bottleneck of the consensus protocol itself. With recent advances in consensus technology, the performance limit has been greatly lifted, typically to thousands of transactions per second. With this, transaction execution has become a new performance bottleneck. Exploiting parallelism in transaction execution is a clear and direct way to address this and to further increase transaction throughput. Although some recent literature introduced concurrency control mechanisms to execute smart contract transactions in parallel, the reported speedup that they can achieve is far from ideal. The main reason is that the proposed parallel execution mechanisms cannot effectively deal with the conflicts inherent in many blockchain applications. In this work, we thoroughly study the historical transaction execution traces in Ethereum. We observe that application-inherent conflicts are the major factors that limit the exploitable parallelism during execution. We propose to use partitioned counters and special commutative instructions to break up the application conflict chains in order to maximize the potential speedup. When we evaluated the maximum parallel speedup achievable, these techniques doubled this limit to an 18x overall speedup compared to serial execution, thus approaching the optimum. We also propose OCC-DA, an optimistic concurrency control scheduler with deterministic aborts, which makes it possible to use OCC scheduling in public blockchain settings.