While programmable NICs allow for better scalability to handle growing network workloads, providing an expressive yet simple abstraction to program stateful network functions in hardware remains a research challenge. We address the problem with FlowBlaze, an open abstraction for building stateful packet processing functions in hardware. The abstraction is based on Extended Finite State Machines and introduces the explicit definition of flow state, allowing FlowBlaze to leverage flow-level parallelism. FlowBlaze is expressive, supporting a wide range of complex network functions, and easy to use, hiding low-level hardware implementation issues from the programmer. Our implementation of FlowBlaze on a NetFPGA SmartNIC achieves very low latenc...